motion in one dimension exercise1

Motion in one dimensions

Q.1. A runner completes one round of a circular path of radius r in 40 seconds. His displacement after 2 minutes20 seconds will be

[1] zero [2] 2 r [3] 2r [4] 7 r

Q.2. An old man goes for morning walk on a semicircular track of radius 40 m; if he starts from one end of the track andreaches to other end, the distance covered by the man and his displacement will respectively be

[1] 126 m, 80 m [2] 80 m, 126 m [3] 80 m, 252 m [4] 252 m, 80 m

Q.3. A body covered a distance of L m along a curved path of a quarter circle. The ratio of distance to displacement is

[1] 2 2

[2] 2 2

[3] 2

[4] 2

Q.4. A passenger travels along a straight line with velocity v1 for first half time and with velocity v2 for next half time, thenthe mean velocity v is given by

[1] 1 2v vv2

[2] 1 2v v v [3] 2

1

vvv

[4] 1 2

2 1 1v v v

Q.5. A car covers a distance of 2 km in 2.5 minute, if it covers half of the distance with speed 40 km/hr, the rest distanceit will cover with speed

[1] 56 km/hr [2] 60 km/hr [3] 50 km/hr [4] 48 km/hr

Q.6. A bicyclist encounters a series of hills. Uphill speed is always v1 and downhill speed is always v2. The totaldistance travelled is , with uphill and downhill portions of equal length. The cyclist's average speed is

[1] 1

2

vv [2]

2

1

vv [3]

1 2

1 2

v vv v [4]

1 2

1 2

2v vv v

Q.7. A motor car covers 13 rd part of total distance with 1v 10km / hr , second

13 rd part with 2v 20 km/hr and

rest 13 rd part with 3v 60km / hr . What is the average speed of the car?

[1] 18 km/hr [2] 45 km/hr [3] 6 km/hr [4] 22.5 km/hr

Q.8. The displacement-time graph for the two particles A and B are straight lines inclined at angles 300 and 600 with thetime axis. The ratio of the velocities of A to B will be

[1] 1 : 2 [2] 1: 3 [3] 3 :1 [4] 1 : 3

Q.9. The velocity-time graph of a body is shown in figure. The displacement covered by the ody in 8 seconds is

[1] 10 m

[2] 9 m

[3] 24 m

[4] 30 m

EXERCISE # 1

(Sec)t1 2 3 4

5 6 7 8

642

-6

(m/s

ec)

Motion in one dimensionsQ.10. The variation of velocity of a particle moving along straight line is shown in figure. The distance traversed by the

body in 4 seconds is

[1] 70 m

[2] 60 m

[3] 40 m

[4] 55 m

Q.11. The displacement y (in metres) of a body varies with time (in seconds) according to the equation

22y t 16t 23

. How long does the body come to rest?

[1] 8 seconds [2] 10 seconds [3] 12 seconds [4] 14 seconds

Q.12. If y denotes the displacement and t denotes the time and the displacement is given by y asin t , the velocity

of the particle is

[1] acos t [2] acos t [3] a cos t [4] acos t

Q.13. A truck travelling due to North at 20 m/s turns East and travels at the same speed. The change in its velocity is

[1] 20 2 m / sNorth East [2] 20 2 m / sSouth East

[3] 40 2 m / sNorth East [4] 20 2 m / sNorth West

Q.14. Which one of the following equations represent the motion of a body with finite constant acceleration. In theseequations y denotes the displacement of the body at time t and a,b and c are the constant of the motion

[1] y = ta

+ bt [2] y at [3] 2y at bt [4] 2 3y at bt ct

Q.15. A car moving at 12 m/s due east attains a speed 16 m/s towards north in 4 seconds. The magnitude of its averageacceleration in m/s2 is

[1] 1 m/s2 [2] 3 m/s2 [3] 5 m/s2 [4] 7 m/s2

Q.16. Adjacent graph shows the variation of velocity of a rocket with time. Find the time of burning of fuel from the graph

[1] 10 sec

[2] 110 sec

[3] 120 sec

[4] cannot be estimated from the graph

Q.17. The adjoining curve represents the velocity-time graph of a particle, its acceleration values along OA, AB and BCin metre/sec2 are respectively

[1] 1,0,–0.5

[2] 1,0,0.5

[3] 1,1,0.5

[4] 1,0.5,0

Time (second)Velo

city

in m

/s

110

120

1000

10

y

x

1 2 3 4O

10

20

velo

city

(m/s

ec)

Time (sec)

A B

2010 30 40C

5 –

10 –

velo

city

in m

/sec

Time in sec

Motion in one dimensionsQ.18. A car travels first 1/3 of the distance AB at 30 km/hr next 1/3 of the distance at 40 km/hr, last 1/3 of the distance

at 24 km/hr. Its average speed in km/hr for the whole jouney is

[1] 40 [2] 35 [3] 30 [4] 28

Q.19. A particle travels A to M along a straight line with a velocity of 8 m/s and M to A with a velocity of 2 m/s, then theaverage velocity for the whole journey is

[1] 3.2 m/s [2] –5 m/s [3] –3.2 m/s [4] 0 m/s

Q.20. An object will continue accelerating untill

[1] the resultant force on it begins to decrease

[2] the velocity changes direction

[3] the resultant force on it is zero

[4] the resultant force is at right angles to its direction of motion

Q.21. A girl walks along an east-west street, and a graph of her displacement from home is as shown in figure. Heraverage velocity for the whole time intervals is

[1] zero

[2] 6 m/min

[3] 11 m/min

[4] 15 m/min

Q.22. The uniform motion in the following acceleration time graph is

[1] AB

[2] BC

[3] CD

[4] DE

Q.23. The displacement-time relationship for a particle is given by 20 1 2x a a t a t . The acceleration of the particle is

[1] 0a [2] 1a [3] 2a [4] 22a

Q.24. A particle travels for 40 seconds under the influence of a constant force. If the distance travelled by the particle isS1 in the first twenty seconds and S2 in the next twenty seconds, then

[1] S2 = S1 [2] S2 = 2S1 [3] S2 = 3S1 [4] S2 = 4S1

Q.25. A particle moves with constant acceleration for 6 seconds after starting from rest. The distance travelled duringthe consecutive 2 seconds interval are in the ratio

[1] 1 : 1 : 1 [2] 1 : 2 : 3 [3] 1 : 3 : 5 [4] 1 : 5 : 9

Q.26. A body having initial velocity u is moving with uniform acceleration a. The distance covered by it in nth second is

[1] au 2n 12

[2] au 2n 12

[3] au 2n 12

[4] au 2n 12

Q.27. A ball is thrown upward and reaches a height of 64 feet, its initial velocity should be (g = 32 ft/sec2)

[1] 64 ft/sec [2] 72 ft/sec [3] 32 ft/sec [4] 4096 ft/sec

t

B

A C

5 10 15 20

min

010203040

–30

distance east

(m)

E

DC

BA10

t8642

51015

a(m/s2)

-5

Motion in one dimensionsQ.28. Two bodies of different masses ma and mb are dropped from two different heights, viz a and b. The ratio of times

taken by the two to drop through these distance is

[1] a : b [2] a

b

m b:m a [3] a : b [4] 2 2a : b

Q.29. A stone weighing 10 kg is dropped from a cliff in a high wind. The wind exerts a steady horizontal force of 50 N onthe stone as it falls. The path that the stone follows will be

[1] A parabola [2] An ellipse

[3] A more complicated path [4] A straight line

Q.30. A body thrown up with a finite speed is caught back after 4 sec. The speed of the body with which it is thrownup is

[1] 10 m/sec [2] 20 m/sec [3] 30 m/sec [4] 40 m/sec

Q.31. A ball is dropped from certain height on a glass floor so that it rebounds elastically to the same height. If theprocess continues, the velocity-time graph for such a motion would be

[1] [2] [3] [4]

Q.32. A stone is thrown vertically upwards with an initial velocity of 30 m/s. The time taken for the stone to rise to itsmaximum height is

[1] 0.326 s [2] 3.26 s [3] 30.6 s [4] 3.06 s

Q.33. A body is thrown upward and reaches its maximum height. At that position

[1] its velocity is zero and its acceleration is also zero

[2] its velocity is zero but its acceleration is maximum

[3] its acceleration is minimum

[4] its velocity is zero and its acceleration is the acceleration due to gravity

Q.34. The initial velocity of a particle (at t = 0) is u and the acceleration of particle at time t is given byf = at. Where a is a constant which of the following relation for velocity v of particle after time t is true?

[1] v = u + at2 [2] v = u + at2/2 [3] v = u + at [4] none of these

Q.35. A man is walking on a road with a velocity 3 km/hr. Suddenly rain starts falling. The velocity of rain is10 km/hr in vertically downward direction. The relative velocity of the rain is

[1] 13 km / hr [2] 7 km / hr [3] 109 km / hr [4] 13 km/hr

Q.36. A boat P is moving at 40 km/hr and another boat Q is moving at 20 km/hr. Which one of the following is not apossible value for their relative velocity


Q.37. The position of a body with respect to time is given by x = 4t3 – 6t2 + 20 t + 12. Acceleration att = 0 will be

[1] –12 units [2] 12 units [3] 24 units [4] –24 units

Q.38. A body travels 200 cm in the first two seconds and 220 cm in the next four second. The velocity at the end of theseventh second from the start will be[1] 10 cm/s [2] 5 cm/s [3] 15 cm/s [4] 20 cm/s

Q.39. A man standing on a road hold his umbrella at 300 with the vertical to keep the rain away. He throws the umbrellaand starts running at 10 km/h. He finds that raindrops are hitting his head vertically, the speed of rain drop withrespect to the road will be[1] 10 km/h [2] 20 km/h [3] 30 km/h [4] 40 km/h

T 2TT 2T

V

t t

V

T 2TT 2T

t t

Motion in one dimensionsQ.40. The linear momentum of a body is p. The linear momentum p varies with time. The equation for variation is

p = a + bt2 where a and b are constants. The effective force acting on the body is[1] proportional to t2 [2] constant [3] proportional to t [4] inversely proportional to t

Q.41. The acceleration of a particle increases linearly as bt with time. If the particle starts from v0 as initial velocity thenthe distance travelled in t seconds will be

[1] 30

1v t bt6

[2] 20

1v t bt6

[3] 30

1v t bt6

[4] 30

1v t bt2

Q.42. A particle has velocity given by v = 20 + 0.1 t2 then it has[1] uniform acceleration [2] uniform retardation[3] non uniform acceleration [4] zero acceleration

Q.43. A body starting from rest and has uniform acceleration 8 m/sec2. The distance travelled by it in 5th second will be[1] 36 m [2] 40 m [3] 100 m [4] 200 m

Q.44. A body starts from rest, the ratio of distances travelled by the body during 3rd and 4th seconds is[1] 7/5 [2] 5/7 [3] 7/3 [4] 3/7

Q.45. A body sliding on a smooth inclined plane requires 4 sec to reach the bottom after starting from rest at the top.How much time does it take to cover one fourth the distance starting from the top[1] 1 sec [2] 2 sec [3] 0.4 sec [4] 1.6 sec

Q.46. The initial velocity of a particle is 10 m/sec and its retardation is 2 m/sec2. The distance covered in the fifth secondof the motion will be[1] 1 m [2] 19 m [3] 50 m [4] 75 m

Q.47. A particle is moving east-wards with a velocity of 5m/sec. In 10 seconds its velocity changes to 5m/sec north-wards. The average acceleration during this time is

[1] 21 m/ sec

2 in N-W direction [2] 21 m/ sec

2 in the N-E direction

[3] 12 m/sec2 in N-W direction [4] 1

2 m/sec2 towards east

Q.48. A ship of mass 3 x 107 kg initially at rest, is pulled by a force of 5 x 104 N through a distance of 3m. Assuming thatthe resistance due to water is negligible, the speed of the ship is[1] 1.5 m/sec [2] 60 m/sec [3] 0.1 m/sec [4] 5 m/sec

Q.49 A particle moves with a constant acceleration such that in the successive time intervals t1 , t2 and t3 itsaverage velocities are v1, v2 and v3. The ratio of v1 – v2 and v2 – v3 is

[1] 1 2 2 3t t : t t [2] 1 2 2 3t t : t t [3] 1 2 2 3t t : t t [4] t1 – t2 : t2 – t3

Q.50 A car travels from place A to the place B at 20 km/hour and returns at 30 km/hour. The average speedof the car for the whole journey is

[1] 25 km/hour [2] 24 km/hour [3] 50 km/hour [4] 5 km/hour

Qus. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ans. 3 1 1 1 2 4 1 4 2 4 3 3 2 3 3Qus. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Ans. 1 1 3 4 3 1 1 4 3 3 4 1 3 4 2Qus. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45Ans. 3 4 4 2 3 1 1 1 2 3 1 3 1 2 2Qus. 46 47 48 49 50Ans. 1 1 3 2 2

ANSWER KEY EXERCISE # 1


Q.1 The velocity-time graph of a linear motion is shown below. The displacement from the origin after8 seconds is

1 2 3 45 6 7 8

-2

-4

0

24

t(sec)u m

/s

[1] 18 m [2] 16 m [3] 6 m [4] 6 cm

Q.2 A train is moving in the north at a speed 10 m/sec. Its length is 150 m. A parrot is flying parallel tothe train in the south with a speed of 5 m/s. The time taken by the parrot to cross the train will be

[1] 12 sec [2] 8 sec [3] 15 sec [4] 10 sec

Q.3 A particle is moving in a plane with velocity given by 0u u i a cos t j , where i and j are unit vectors

along x and y axes respectively. If particle is at the origin at t = 0. Calculate the trajectory of the particle

[1] 0uy asinx

[2]

0

xy asinu

[3]

0u1y .sina x

[4]

0

1 xy .sina u

Q.4 In the following velocity-time graph of a body, the distance and displacement travelled by the body in 5second in meters will be

1 2 3

40

302010

0

-10

-20

-30

4 5 t(sec)

[1] 70, 110 [2] 110, 70 [3] 40, 70 [4] 90, 50

Q.5 A runner completes one round of a circular path of radius r in 40 sec. His displacement after 2 minutes20 sec. will be -

[1] zero [2] 2 r [3] 2r [4] 7 r

Q.6 The displacement is given by x = 2t2 + t + 5, the acceleration at t = 5 sec will be

[1] 8 m/s2 [2] 12 m/s2 [3] 15 m/s2 [4] 4 m/s2

Q.7 A part icle m oves along the x-axis in such a way that its x-coordinate var ies with t im e asx = 2 – 5t + 6t2. The initial velocity and accleration of particle will respectively be

[1] –5 m/s, 12 m/s [2] 5 m/s, –12 m/s [3] –5 m/s, –12 m/s [4] 5 m/s, 12 m/s

Q.8 Two trains each of length 50 m, are approaching each other on parallel rails. Their velocities are 10 m/s and15 m/s. They will cross each other in

[1] 2 sec [2] 4 sec [3] 10 sec [4] 6 sec

Q.9 A car travels a distance of 2000m. If the first half distance is covered at 40 km/hour and the secondhalf at velocity v and if the average velocity is 48 km/hour then the value of v is

[1] 56 km/hour [2] 60 km/hour [3] 50 km/hour [4] 48 km/hour

EXERCISE # 2

Motion in one dimensionsQ.10 The following figures show some velocity V versus time t curves. But only some of these can be realised

in practice. These are

t

V

O t

V

O t

V

O t

V

O

(a) (b) (c) (d)

[1] Only a,b and d [2] only a,b,c [3] only b and c [4] all of them

Q.11 At an instant t, the coordinates of a particle x = at2, y = bt2 and z = 0, then its velocity at the instant t will be

[1] t 2 2t a b [2] 2t 2 2t a b [3] 2 2a b [4] 2 2 22t a b

Q.12 Figure shows the position of a particle moving on the x-axis as a function time

[1] the particle has come to rest 6 times

[2] the maximum speed is at t = 6 sec

[3] the velocity remains positive for t = 0 to t = 6 sec

[4] the average velocity for the total period show in negative

Q.13 A rocket is projected vertically upwards and its time velocity graph is shown in the figure. The maximumheight attained by the rocket is

20 t(sec)120V

(M/sec)

1000

[1] 1 km [2] 10 km [3] 100 km [4] 60 km

Q.14 A stone is dropped into a well and the sound of impact of stone on the water is heard after 2.056 secof the release of stone fro the top. If acceleration due to gravity is 980 cm/sec2 and velocity of soundin air is 350 m/s, calculate the depth of the well

[1] 1.96 m [2] 19.6 m [3] 6.91 m [4] 69.1 m

Q.15 A body is dropped from a height h under acceleration due to gravity g. If t1 and t2 are time intervals forits fall for first half and the second half distance, the relation between them is

[1] t1 = t2 [2] t1 = 2t2 [3] t1 = 2.414 t2 [4] t1 = 4t2

Q.16 A rocket is launched from the earth surface so that it has an acceleration of 19.6 m/s2. If its engineis switched off after 5 seconds of its launch, then the maximum height attained by the rocket will be

[1] 245 m [2] 490 m [3] 980 m [4] 735 m

Q.17 If the relation between distance x and time t is denoted by 2t x x where and are constant

quantities, the deceleration of the particle is

[1] 32 v [2] 3v [3] 32 v [4] 2 32 v

Q.18 A particle is moving so that its displacements is given as 3 2s t 6t 3t 4 meter. Its velocity at the

instant when its acceleration is zero will be

[1] 3 m/s [2] –12 m/s [3] 42 m/s [4] –9 m/s

642

10

20

t (sec)

Disp

lacem

ent


Q.19 A car starts from rest and has an acceleration a t . A truck is moving with a uniform velocity of

4 m/s. At what distance will the car overtake the truck? (at t = 0 both start their motion in the samedirection from the same position)

[1] 16 m [2] 8 m [3] 32 m [4] 4 m

Q.20 An object is released from some height. Exactly after one second, another object is released from thesame height. The distance between the two objects exactly after 2 secodns of the release of secondobject will be

[1] 4.9 m [2] 9.8 m [3] 19.6 m [4] 24.5 m

Q.21 A ball is thrown from the ground with a velocity of 80 ft/sec. Then the ball will be at a height of 96 feetabove the ground after time

[1] 2 and 3 sec [2] only 3 sec [3] only 2 sec [4] 1 and 2 sec

Q.22 A man standing on the edge of a cliff throws a stone straight up with initial speed u and then throwsanother stone straight down with same initial speed u from the same position. Find the ratio of speeds,the stone would have attained when they hit the ground at the base of the cliff?

[1] 2 : 1 [2] 1 : 2 [3] 1 : 1 [4] 3 : 1

Q.23 A stone is dropped from a bridge and it reaches the ground in 4 seconds. The height of the bridge is

[1] 78.4 m [2] 64 m [3] 260 m [4] 2000 m

Q.24 A stone is dropped from the top of a tower and it strikes with 3 km/hr against the ground. Another stoneis thrown vertically downwards from the same top of the tower with a velocity 4 km/hr. Its velocity whenit strikes the ground will be

[1] 7.0 km/hr [2] 5.0 km/hr [3] 3.5 km/hr [4] 4.0 km/hr

Q.25 A stone is thrown vertically upwards from the top of a tower with a velocity u and it reaches the groundwith a velocity 3u. The height of the tower is

[1] 23u

g [2] 24u

g [3] 26u

g [4] 29u

g

Q.26 The displacement of a particle as a function of time is shown in fig.The fig. indicates that

0 1 2 3 4 x

Dis

tanc

e

y

Time

t

[1] the particle starts with a certain velocity, but the motion is retarded and finally the particle stops

[2] the velocity of particle is constant throught

[3] the acceleration of the particle is constant throughout

[4] the particle starts with a constant velocity, the motion is accelerated and finally the particle moveswith another constant velocity.

Q.27 The acceleration of a partic le, starting from rest, varies with time according to the relationa = kt + c. Then the velocity v of the particle after a time t will be

[1] 22kt ct [2] 21 kt ct2

[3] 2kt ct [4] 21 kt ct2


Q.28 The velocity of a particle moving in the positive direction of x-axis varies as v x where is positive

constant. Assuming that at the moment t = 0, the particle was located at x = 0 the value of time dependenceof the velocity and the acceleration of the particle

[1] 2 2

t 1,2 2

[2] 2 2t ,2 2

[3] 2

2t

, 22

[4] None of these

Q.29 Three points are located at the vertices of an equilateral triangle whose side equals a. They all startmoving simultaneously with velocity V constant in magnitude. With the first point heading continuouslyfor the second, the second for the third and the third for the first. How soon will the points coverage?

[1] 3Va [2]

2a3V [3]

a3V [4]

aV

Q.30 Two bodies of masses m1 and m2 are dropped from height h1 and h2 respectively. They reach the groundafter time t1 and t2 respectively. Which of the following relation is correct

[1]

1/ 2

1 1

2 2

t ht h

[2] 1 1

2 2

t ht h

[3]

1/ 2

1 1

2 2

t mt m

[4] 1 1

2 2

t mt m

Q.31 Which of the following statements is wrong about a ball thrown vertically up?

[a] it is moving with constant acceleration

[b] it may have different velocities at the same position

[c] it may have two positions at the same time

[d] the angular momentum of the particle about origin remains conserved

[1] c only [2] c, d [3] b, c, d [4] a, b, c and d

Q.32 A particle is projected vertically upwards and it reaches the maximum height H in time T seconds. Theheight of the particle at any time t will be

[1] 2g t T [2] 21H g t T2

[3] 21 g t T2

[4] H g t T

Q.33 A rocket is fired vertically upwards such that its engine takes 10 seconds in exploding fully. Its velocitytime curve is shown in the figure. The height reached by the rocket is

10 20 30 40 50Time (in sec)

V elo

city

in m

/s 1000

500

[1] 20 kms [2] 40 kms [3] 400 kms [4] 1000 kms

Q.34 If the displacement of a particle varies with time according to the relation Kx [1 exp bt ]b

, then the

velocity (V) of the particle is

[1] V K exp bt [2] KV exp btb

[3] )btexp(b

KV2

[4] 2

KV exp btb


Q.35 If velocity of a particle is given by 2V 10 2t m / s . The average acceleration between 2 and 5 s is

[1] 2 m/s2 [2] 4 m/s2 [3] 12 m/s2 [4] 14 m/s2

Q.36 A body of mass 3 kg falls from the multistoreyed building 100 m high and buries itself 2 meters deepin the sand. The time of penetration will be

[1] 9 sec. [2] 0.9 sec. [3] 0.09 sec. [4] 10 sec.

Q.37 A body travelling with uniform acceleration crosses two points A and B with velocities 20 m/sec and30 m/sec respectively. Then the speed of the body at mid-point of A and B is

[1] 25 m/sec [2] 25.5 m/sec [3] 24 m/sec [4] 10 6 m/sec

Q.38 Two mirrors, mounted vertically, are made to move towards each other with a speed v m/s each. A particle that canbounce back between the two mirrors starts from one mirror when the mirrors are d meters aprat. On reaching thesecond mirror, it bounces back and so on. If the particle keeps on travelling at a constant speed of 3 v m/s, howmany trips can it make before the mirrors run into each other and what total distance does it cover

[1] ,5.1d [2] ,1.5d [3] 0,6.1d [4] 0,1.6d

Q.39 Two trains each having a speed of 30 km/hour are headed at each other on the same straight track. Abird that can fly at 60 km/hour flies off from one train when they are 60 km apart and heads directly forthe other train. On reaching the other train it flies directly back to the first, and so fourth then the totaldistance travelling by the bird is

[1] 40 km [2] 60 km [3] 80 km [4] 100 km

Q.40 The distance covered by the body in time 't' is proportional to the square of the time 't'. The accelerationof the body is

[1] increasing [2] decreasing [3] zero [4] constant

Q.41 If the displacement of a particle varies with time as x t 7 , the

[1] velocity of the particle is inversely porportional to t [2] velocity of the particle is proportional to t

[3] velocity of the particle is proportional to t [4] the particle moves with a constant acceleration

Q.42 Between two stations a train accelerates uniformly at first, then moves with constant speed and finallyretards uniformly. If the ratios of time taken are 1 : 8 : 1 and the greatest speed is 60 km/hour. Thenthe average speed over the whole journey


Q.43 A car accelerates from rest at a constant rate for some time after which it decelerates at a constant

rate to come to rest. The maximum velocity V reached if total time taken (t seconds) is given by

[1] V t

[2] 2

V t

[3]

2

V t

[4] V t

Q.44 The distance x travelled by the car in above problem in time 't' is given by

[1] 2tx2

[2]

2x t

[3] 2x t

[4]

2tx2

Q.45 A ball is thrown vertically upwards with a velocity of 30 m/s. If the acceleration due to gravity is10 m/s2, what will be the distance travelled by it in the last second of motion.

[1] 5 m [2] 10 m [3] 25 m [4] 30 m

Motion in one dimensionsQ.46 Two balls are dropped from different heights. One ball is dropped 2 sec after the other but they both

strike the griound at the same time, 3 sec after the first is dropped. The difference in the heights atwhich they were dropped is

[1] 7.8 m [2] 78 m [3] 15.6 m [4] 39.2 m

Q.47 If a body travels half its total path in the last second of its fall from rest then the time and height of its fall are

[1] 3.41 sec, 57 m [2] 4.31 sec, 57 m [3] 1.34 sec, 57 m [4] 3.14 sec, 75 m

Q.48 From the foot of a tower 90 m high, a stone is thrown up so as to reach the top of the tower. Two secondlater another stone is dropped from the top of the tower. The two stones will meet at

[1] 83.6 m [2] 38.6 m [3] 63.8 m [4] 68.3 m

Q.49 Two bodies are thrown vertically upward, with the same initial velocity of 98 m/s but 4 sec apart. Howlong after the first one is thrown will they meet?

[1] 10 sec [2] 11 sec [3] 12 sec [4] 13 sec

Q.50 A ball is thrown vertically upwards from the top of a tower with a velocity of 10 m/sec. If the ball fallson the ground after 5 seconds, the height of the tower will be

[1] 25 m [2] 50 m [3] 75 m [4] 100 m

Q.51 In the above question, what height above the tower will the ball attain?

[1] 5 m [2] 5 m [3] 5 2 m [4] 10 m

Q.52 In the above question, the total distance travelled by the ball before it returns to the ground is

[1] 85 m [2] 75 m [3] 100 m [4] 175 m

Q.53 In the above question, in what time will it reach the maximum height

[1] 1 sec [2] 2 sec [3] 2 sec [4] 1/ 2 sec

Q.54 In the above question, with what velocity will the ball strike the ground

[1] zero [2] 40 m/s [3] 10 m/s [4] 60 m/s

Q.55 A stone is dropped from the top of the tower and travels 24.5 m in the last second of its journey. Theheight of the tower is

[1] 44.1 m [2] 49 m [3] 78.4 m [4] 72 m

Q.56 Two balls are dropped from the same point after an interval of 1 s. If acceleration due to gravity is 10m/s2, what will be the separation 3 seconds after the release of first ball?

[1] 5 m [2] 10 m [3] 25 m [4] 30 m

Q.57 Two balls of equal masses are thrown upwards along the same vertical direction at an interval of 2 seconds.With the same initial velocity of 39.2 m/sec. Then these collide at a height of

[1] 117.6 m [2] 73.5 m [3] 196.0 m [4] 44.1 m

Q.58 The speed v of a particle movign along a straight line, when it is at a distance x from a fixed point onthe line is given by v2 = 108 x – 9x2 . Then magnitude of its acceleration when it is at a distance 3 metrefrom the fixed point is

[1] 9 m/s2 [2] 18 m/s2 [3] 27 m/s2 [4] None of these

Q.59 A body is thrown up in a lift with a velocity u relative to the lift and the time of flight is found to be 't'.The acceleration with which the lift is moving up will be

[1] u gt

t

[2] u gt

t

[3] 2u gt

t

[4] 2u gt

t

Motion in one dimensionsQ.60 A body dropped from the top of a tower covers 7/16 of the total height in the last second of its fal l. The

time of fall is

[1] 2 sec [2] 4 sec [3] 1 sec [4] 50 sec7

Q.61 A person standing on the roof of a house of height h throws a particle vertically downwards and other particlein a horizontal direction with the same speed u. The ratio of speeds of the particles on reaching the earth is

[1] 2gh : u [2] 1 : 2 [3] 2 :1 [4] 1 : 1

Q.62 In the above question, the ratio of vertical components of the velocities will be

[1] one [2] more than one [3] less than one [4] will depend on mass

Q.63 In the above question the first particle instead of being thrown downwards, is thrown upwards with thesame velocity. The ratio of the velocities of the particles on reaching the earth, will be

[1] 1 : 1 [2] 2 :1 [3] 2 : 1 [4] 1 : 4

Q.64 Juggler keeps on moving four balls in the air continuously such that each ball attains 20 m height. Whenthe first ball leaves his hand, the position of the other balls ( in metre height) will be

[1] 10, 20, 10 [2] 15, 20, 15 [3] 5, 51, 20 [4] 5, 10, 20

Q.65 The retardation of a motor boat after its engine is switched off, is given by dvdt = – kv3

0, where k is a

constant and v0 is its velocity at the time of shutting off of the engine. The velocity of the motor boatafter time t will be

[1] 0

20

v2v kt 1 [2] kt

0v e [3] 0v2 [4] v0

Q.66 A part ic le m oves with constant speed v along a regular hexagon ABCDEF in same order(ie., A to B, B to C, C to D, D to E, E to F, F to A....) Then magnitude of average velocity for its motionfrom A to C

[1] V [2] V/2 [3] 3V / 2 [4] None of these

Q.67 The acceleration (a) of moving particle varies with displacement according to the following relation 2a x 3x .Then correct relation between velocity and displacement is (where C = constant)

[1] 3 2x 3xV C

3 2 [2] 3 22V x 3x C

3

[3] 3 22V x 3x C

3

[4] V = 2x + 3

Q.68 If a point moves in a straight line in such a manner that its retardation is proportional to its speed, thedistance covered (x) is assosciated with speed (V) is

[1] x V [2] 2x V [3] 3x V [4] x V

Q.69 A ball is dropped from a height of 20 m and rebounds with a velocity which is 3/4th of the velocity with whichit hits the ground. What is the time interval between the first and second bounces (g = 10 m/s2)

[1] 3 sec [2] 4 sec [3] 5 sec [4] 6 sec


Q.70 A river is flowing from west to east at a speed of 5 metres/minute. A man on the south bank of theriver, capable of swimming at 10 metres/min. in still water, wants to swim across the river in shortesttime. He should swim in a direction

[1] due north [2] 300 east of north [3] 300 west of north [4] 600 east of north

Q.71 A particle moves along a circle with a uniform speed v. After it has made an angle of 600, the change in itsspeed will be

[1] v 2 [2] v2 [3] v 3 [4] 0

Q.72 A boat moves relative to water a velocity which is 1/n times the river flow velocity. At what angle to thestream direction must be boat move to minimize drifting?

[1] / 2 [2] 1 1sinn

[3] 1sin 1/ n2

[4] 1sin 1/ n

2

Q.73 A particle moves with a v in a horizontal circular path. The change in its velocity for covering 600 will be

[1] v 2 [2] v / 2 [3] v 3 [4] v

Q.74 A car A is goving north-east at 80 km/hr. and antoher car B is going south-east at 60 km/hr. Then thedirection of the velocity of A relative to B makes with the north an angle such that tan is

[1] 1/7 [2] 3/4 [3] 4/3 [4] 3/5

Q.75 The motion of particle is defined by x acos t and y asin t . The acceleration of particle is

[1] a [2] 2a [3] –a2 [4] 2 2a

Q.76 A boat man could row his boat with a speed 10 m/sec. He wants to take his boat from P to a point Q justopposite on the other bank of the river flowing at a speed 4 m/sec. He should row his boat

[1] at right angle to the stream

[2] at an angle of 1sin 2 / 5 with PQ up the stream

[3] at an angle of 1sin 2 / 5 with PQ down the stream

Q

P

V =4m/ss

[4] at an angle of 1cos 2 / 5 with PQ down the stream

Q.77 A particle is executing a circular motion of radius R with a uniform speed v. After completing half the circle,the change in velocity and in speed will be respectively

[1] zero, zero [2] 2 v, zero [3] 2 v, 2 v [4] zero, 2 v

Q.78 A balloon is at a height of 81 metres and is ascending upwards with a velocity of 12 m/s. A body of 2 kgweight is dropped from it. If g = 10 m/s2, the body will reach the surface of the earth in

[1] 1.5 sec [2] 4.025 sec [3] 5.4 sec [4] 6.75 sec

Q.79 If the position vector of a particle is kj4it3r

, the particle will be

[1] moving with uniform velocity [2] stationary

[3] moving with uniform acceleration [4] insufficient data

Q.80 A bullet loses 1

20 of its velocity in passing through a plank. The least number of planks required to stop the

bullet is -

[1] 10 [2] 11 [3] 12 [4] 23


Q.81 The motion of a body falling from rest in a resisting medium is described by the equation dv a bvdt

, where

a and b are constants. The velocity at any time t is -

[1] btt

av (1 e )b

[2] btt

bv ea

[3] btt

av (1 e )b

[4] btt

bv ea

Q.82 A ball is thrown vertically upwards. It was observed at a height h twice with a time interval t. The initialvelocity of the ball is -

[1] 2 28gh g ( t) [2] 2g t8gh

2

[3] 2 21 8gh g ( t)2

[4] 2 28gh 4g ( t)

Q.83 A stone falls freely from a point O. It passes through the points P, Q, R ....... such that OP, OQ, OR,.... arein geometric progression. Then velocities of stone at P, Q, R.... are in -

[1] arithmetic progression [2] geometric progression

[3] harmonic progression [4] logarithmic mean

Q.84 A ship of mass 3 × 107 kg, initially at rest, is pulled by a force of 5 × 104N through a distance of 3m.Assuming that the resistance due to water is negligible, the speed of the ship is -

[1] 1.5 ms–1 [2] 60 ms–1 [3] 0.1 ms–1 [4] 5 ms–1

Q.85 An elevator whose floor to ceilling distance is l is ascending with uniform acceleration it. At some instant(say t = 0), a loose bolt drops from its ceiling. The time taken by the bolt to hit the floor is -

[1] 2

g a

[2] 2g

[3] 2

g a

[4] 2a

Qus. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ans. 3 4 2 2 1 4 1 2 2 1 2 1 4 2 3Qus. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Ans. 4 1 4 1 4 1 3 1 2 2 1 2 2 2 1Qus. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45Ans. 1 2 1 1 4 3 2 2 2 4 4 2 4 4 3Qus. 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60Ans. 4 1 1 3 3 2 1 1 2 1 3 2 3 3 2Qus. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75Ans. 4 2 1 2 1 3 2 4 1 1 4 3 4 1 3

Qus. 76 77 78 79 80 81 82 83 84 85Ans. 2 2 3 1 2 1 3 2 3 3

ANSWER KEY EXERCISE # 2


Q.1 The displacement time graph for two particles A and B are straight lines inclined at angles of 300 and 600 with the

time axis. The ratio of velocity of A BV : V is [CPMT-1990]

[1] 1 : 2 [2] 1: 3

[3] 3 :1 [4] 1 : 3

Q.2 An elevator car, whose floor to celling distance is equal to 2.7 m, starts ascending with constant acceleration of1.2 ms-2. 2 sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is

[CET Karnataka-94]

[1] 0.54 s [2] 6 s [3] 0.7 s [4] 1s

Q.3 A body 'A' is dropped vertically from the top of a tower. If another identical body 'B' is projected thrown from thesame point at the same instant, then

[1] 'A' will reach the ground earlier than 'B'

[2] 'B' will reach the ground earlier than 'A'

[3] Both 'A' and 'B' will reach the ground simultaneously

[4] none of these

Q.4 A body is dropped from the top of a tower with zero velocity and reaches ground in 4 seconds. The height of thetower is about [g = 10 m/s2] [AFMC-94]

[1] 20 m [2] 40 m [3] 80 m [4] 160 m

Q.5 The time displacement graph of a moving particle is shown as the instantaneous velocity is negative of the point

[1] D [AFMC-94; CBSE-94]

[2] F

[3] C

[4] E

Q.6 A balloon is at a height of 81 m and is ascending upwards with a velocity of 12 m/s. A body of 2 kg weight isdropped from it. If g = 10 m/s2, the body will reach the surface of the earth in

[1] 1.5 s [2] 4.025 s [3] 5.4 s [4] 6.75 s [RPMT-94]

Q.7 The initial velocity of a body moving along a straight line is 7 m/s. It has a uniform acceleration of 4 m/s2. Thedistance covered by the body in the 5th second of its motion is [RPMT-94]

[1] 25 m [2] 35 m [3] 50 m [4] 85 m

Q.8 A body is projected up to with a speed 'u' and the time taken by it is T to reach the maximum height H. Pick outthe correct statement [EAMCET-95]

[1] It reaches H/2 in T/2 sec [2] It acquires velocity u/2 in T/2 sec

[3] Its velocity is u/2 at H/2 [4] Same speed at 2T

TIME

DIS

PLAC

EMEN

T

F

E

D

C

EXERCISE # 3

A

B

))

t

s

O300

600

Motion in one dimensionsQ.9 A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals of 4 sec

each. Its initial velocity is [MP PET-95]

[1] 1 m/sec [2] 10 m/sec [3] 5 m/sec [4] 2 m/sec

Q.10 A rocket is f ired upward from the earth's surface such that it creates an acceleration of19.6 m/sec2. If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface wouldbe [MP PET- 95]

[1] 245 m [2] 490 m [3] 980 m [4] 735 m

Q.11 A ball is thrown upwards with a velocity of 100 m/sec. It will reach the ground after [AFMC-95]

[1] 40 sec [2] 20 sec [3] 10 sec [4] 5 sec

Q.12 The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with aninitial velocity v0. The distance travelled by the particle in time t will be [BHU-95,CPMT-95]

[1] 30

1v t bt6

[2] 30

1v t bt3

[3] 20

1v t bt3

[4] 20

1v t bt2

Q.13 The displacement of a body is given to be proportional to the cube of time passed. The magnitude of the accelerationof the body, is [AIIMS-96]

[1] Increasing with time [2] Decreasing with time

[3] Constant but not zero [4] Zero

Q.14 A particle starts from rest and moves with uniform acceleration. Then the ratio of distance covered in nth sec. to nsec. is [RPET-96]

[1] 2n

2n 1[2] 2

2 1n n [3]

2nn 1

[4] 2

2n 1n

Q.15 A car moves for half of its time at 80 km/h and for rest half of time at 10 km/h. Total distance covered is 60 km.What is the average speed of the car [RPET-1996]

[1] 60 km/h [2] 45 km/h [3] 120 km/h [4] 180 km/h

Q.16 A body dropped from a height h with initial velocity zero, strikes the ground with velocity 3 m/s. Another body ofsame mass is dropped from the height h with an initial velocity of 4 m/s. Find the final velocity with which it strikesthe ground [CPMT-96]

[1] 3 m/s [2] 4 m/s [3] 5 m/s [4] 12 m/s

Q.17 If a body starts from rest and travels 1.2 m in the 8th second then what is the acceleration [AFMC-97]

[1] 0.20 m/s2 [2] 0.16 m/s2 [3] 0.08 m/s2 [4] 0.2255 m/s2

Q.18 A train is moving with uniform velocity. Suddenly, a compartment is separated and still train is moving with samevelocity the compartment moves to a ceratin distance and comes to rest. The distance travelled by the compartmentis how much times of the distance travelles by the train in the same time [RPET-97]

[1] one fourth [2] Half [3] Equal [4] In uncertain ratio

Q.19 A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if twostones are thrown [one upwards and other downwards] with the same velocity u and they reach the earth surfaceafter t1 and t2 seconds respectively, then [CPMT-97]

[1] 1 2t t t [2] 1 2t tt2

[3] 1 2t t t [4] 2 21 2t t t

Motion in one dimensionsQ.20 By which velocity a ball be projected vertically so that the distance it covers in its 6 second is twice the distance

it covers in its 6th second -(g = 10 m/s2) [CPET-2002,CPMT-97]

[1] 58.8 m/s [2] 49 m/s [3] 65 m/s [4] 17.5 m/s

Q.21 The coordinates of a moving particle at any time are given by 2x at and 2y bt . The speed of the particle at

any moment is [EAMCET-93, CPMT-97]

[1] 2t a b [2] 2 22t a b [3] 2 2t a b [4] 2 22t a b

Q.22 A particle experience a constant acceleration for 20 sec after starting from rest. If it travels a distance S1 in thefirst 10 sec and a distance S2 in the next sec, then [CPMT-97]

[1] 1 2S S [2] 21

SS3

[3] 21

SS2

[4] 21

SS4

Q.23 A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom, starting from rest at the top.How much time does it take to cover one-fourth the distance starting from rest at the top [BHU-98]

[1] 1 sec [2] 2 sec [3] 4 sec [4] 16 sec

Q.24 A ball released from a great height falls freely towards earth. Another body is released from the same height exactlyone second later. The separation between the two bodies after two second the release of the second body is

[BHU-98]

[1] 9.8 m [2] 49 m [3] 24.5 m [4] 19.6 m

Q.25 A car moving with a speed of 40 km/hr can be stopped by applying breaks after atleast 2m. If the same car ismoving with a speed of 80 km/h. What is the minimum stopping distance [CBSE-98]

[1] 8 m [2] 2 m [3] 4 m [4] 6 m

Q.26 A car travels half distance with 40 km/hr and rest half distance with 60 km/hr., then the average speed of car is

[1] 40 km/hr [2] 48 km/hr [3] 52 km/hr [4] 60 km/hr [RPET-98]

Q.27 A car moves along a straight line whose equation of motion is given by 2 3s 12t 3t 2t , where[s] is in metres

and [t] in seconds. The velocity of the car at start will be [CPMT-98]

[1] 7 m/s [2] 9 m/s [3] 12 m/s [4] 16 m/s

Q.28 A stone is thrown with an initial speed of 4.9 m/s from a bridge in vertically upward direction. It falls down in waterafter 2 sec. The height of the bridge is [AFMC-99]

[1] 4.9 m [2] 9.8 m [3] 19.8 m [4] 24.7 m

Q.29 Two car A and B are initially at rest. Now car A starts moving with a constant velocity of 40 m/s and car B startsmoving with constant acceleration of 4 m/s2. How much time will have lapsed from before the cars again meet

[RPET-99]

[1] 15 second [2] 20 second [3] 30 second [4] 35 second

Q.30 A wheel covers a distance of 9.5 km in 2000 revolutions. The diameter of the wheel is [RPMT-99]

[1] 15 cm [2] 7.5 cm [3] 1.5 m [4] 7.5 m

Q.31 Two trains, each 50 m long are travelling in opposite with velocity of 15 m/s. The time of crossing is[ CPMT-99]

[1] 2 s [2] 10 s3 [3] 2 3 s [4] 4 3 s


Q.32 The displacement of a particle is given by 2 4y a bt ct dt . The initial velocity and acceleration are respectively

[1] b,–4d [2] –b, 2c [3] b, 2c [4] 2c, –4d [CPMT-99]

Q.33 A stone is allowed to fall from from the top of a tower and covers half the height of the tower in the last second ofits journey. The time taken by the stone to reach the foot of the tower is [CPMT-99]

[1] 2 2 s [2] 2 2 s [3] 4s [4] 2 2 s

Q.34 A man throws a ball vertically upward and it rises through 20 m and returns to his hands. What was the initialvelocity (u) of the ball and for how much time (T) it remained in the air (g = 10 m/s2) [MPPET-2001]

[1] u = 10 m/s, T = 2s [2] u = 10 m/s, T = 4s [3] u = 20 m/s, T = 2s [4] u = 20 m/s, T = 4s

Q. 35 A balloon starts rising from the ground with an acceleration of 1.25 m/s2. After 8s, a stone is released from theballoon. The stone will ( taking g = 10 ms-2) [Karnataka-2001]

[1] Have a displacement of 50 m [2] Cover a distance of 40 m in reaching the ground

[3] Reach the ground in 4s [4] Begin to move down after being released

Q. 36 A very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball isthrown when the previous one is at the maximum height. If the maximum height is 5m, the number of balls thrownper minute is (take g = 10 ms-2) [Karnataka-2002]

[1] 120 [2] 80 [3] 60 [4] 40

Q. 37 Initially a body is at rest. If its acceleration is 5 m/s2, then calculate the distance travelled in the 18th sec

[1] 86.5 m [2] 87.5 m [3] 88 m [4] 89 m [AFMC-2001]

Q.38 A particle is moving with velocity 5 m/s towards east and its velocity changes to 5 m/s north in 10 sec. Find theacceleration. [UP-CPMT-2001]

[1] 2 N W [2] 1 N W2

[3] 1 N E2

[4] 2 N E

Q.39 A stone is dropped from a running bus. It will travel towards the ground in a [BHU-2000]

[1] straight line [2] circular path [3] parabolic path [4] none of these

Q.40 A force of 1000 N is applied on a body of mass 100 kg moving with a velocity of 5 m/s. How much time does itrequire to acquire a velocity of 25 m/s [Manipal-2000]

[1] 2 sec [2] 4 sec [3] 6 sec [4] 8 sec

Q.41 If a freely falling body travels in the last second, a distance equal to the distance travelled by it in the first threeseconds, the time of its travel is [Manipal-2000]

[1] 3 sec [2] 4 sec [3] 5 sec [4] 6 sec

Q.42 A packet is dropped from a balloon which is going upward with a velocity 12 m/sec. The velocity of the packet after2 seconds will be [Manipal-2000]

[1] –7.6 m/sec [2] 7.6 m/sec [3] 12 m/sec [4] –12 m/sec

Q.43 If a ball is thrown vertically upwards at 40 m/s, its velocity after two seconds will be [AIIMS2000]

[1] 10 m/s [2] 20 m/s [3] 30 m/s [4] 40 m/s

Q.44 Velocity-time curve for a body projected vertically upwards is [AIIMS-2000]

[1] Ellipse [2] Parabola [3] Hyperbola [4] Straight line

Motion in one dimensionsQ.45 A motorcycle is moving with a velocity 80 km/hr ahead of a car moving with a velocity of 65 km/hr in the same

direction. What is the relative velocity of the motorcycle with respect to the car [AFMC-2000]


Q.46 A body starts from rest and has an acceleration 20 cm/sec2. What is the distance covered by the body infirst 8 sec [AFMC-2000]

[1] 160 cm [2] 640 cm [3] 1280 cm [4] 1640 cm

Q.47 The speed of a boat is 5 km/hr in still water. If it crosses a river of width 1 km along the shortest possible path in15 minutes, then velocity of the river is [AFMC-2000]


Q.48 A particle travels 10 m in first 5 sec and 10 m in next 3 sec. Assuming constant acceleration what is the distancetravelled in next 2 sec [RPET-2000]

[1] 8.3 m [2] 9.3 m [3] 10.3 m [4] None of these

Q.49 The displacement [s] of a body is directly proportional to the square of the time [t] than the acceleration ofthe body is [RPMT-2000]

[1] increases [2] constant [3] decreases [4] zero

Q.50 A train covers 50 metre distance and stops when applied the breaks. If the velocity of train is just doubled andapplied the same retarding force then the distance covered by the train is [RPMT-2000]

[1] 50 m [2] 100 m [3] 150 m [4] 200 m

Q.51 Equation of position [x] with time [t] is given by equation x = 3t3 + 7t2 + 5t + 8. The acceleration at time t = 1s. is

[1] 18 m/s2 [2] 32 m/s2 [3] Zero [4] 14 m/s2 [CPMT-2000]

Q. 52 A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to aheight d/2. Neglecting subsequent motion and air resistance, its velocity v varies with the height h above theground as [IIT-2000]

[1] h

v

d[2] h

v

d [3] h

v

d [4] h

v

d

Q.53 A particle moves according to above velocity time graph. Then what is the ratio between distance travelled in last2 seconds and 7 second [RPET-2001]

[1] 14 [2]

12

[3] 18 [4]

16

Q.54 For a freely falling body ratio of distances travelled in first, second and third second of its motion will be[RPET-2001]

[1] 5 : 3 : 1 [2] 1 : 4 : 9 [3] 1 : 3 : 5 [4] 9 : 4 : 1

Q.55 50 m long trains are crossing each other in opposite direction with velocity of 10 m/s and 15 m/s respectively. Thentime-taken by trains to cross each other will be [RPET-2001]

[1] 2 sec [2] 4 sec [3] 6 sec [4] 8 sec

1 3 5 7 sec

10

m/sec

Motion in one dimensionsQ.56 A particle moves in east with velocity of 15 m/s for 2 sec. then moves northward with 5 m/s for

8 sec, then average velocity of the particle is [RPMT-2001]

[1] 1 m/s [2] 5 m/s [3] 7 m/s [4] 10 m/s

Q.57 A particle is thrown vertically upward. Its velocity at half of the height is 10 m/s, then maximum height attained byit (g = 10 m/s2) [CPMT-2001]

[1] 8 m [2] 20 m [3] 10 m [4] 16 m

Q.58 A body starts from rest with acceleration a = 2[t – 1] then its velocity after 5 seconds will be [RPET-2002]

[1] 15 m/s [2] 25 m/s [3] 35 m/s [4] 45 m/s

Q.59 A point P consider at contact point of a wheel on ground which rolls on ground without sliping then value ofdisplacement of point P when wheel completes half of rotation - [If radius of wheel is 1 m] [CPMT-2002]

[1] 2 m [2] 2 4 m [3] m [4] 2 2 m

Q.60 A car, moving with a speed of 50 km/hr. can be stopped by brakes after at least 6 m. If the same car is moving ata speed of 100 km/hr, the minimum stopping distance is [CPET-2003]

[1] 24 m [2] 6 m [3] 12 m [4] 18 m

Q.61 The coordinates of a moving particle at any time 't' are given by 3x t amd 3y t . The speed of the particle

at time 't' is given by [CPET-2003]

[1] 2 2 2t [2] 2 2 [3] 2 23t [4] 2 2 23t

Q.62 A man throws balls with the same speed vertically upwards one after the other at an interval of2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (g = 9.8m/s2) [CPMT-2003]

[1] only with speed 19.6 m/s [2] more than 19.6 m/s

[3] at least 9.8 m/s [4] any speed less than 19.6 m/s

Q.63 If a ball is thrown vertically upwards with sped u, the distance covered during the last t seconds of its ascent is

[1] ut [2] 21 gt2 [3] 21ut gt

2 [4] u gt t [CPMT-2003]

Q.64 A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for anydisplacement x is proportional to [AIEEE-2004]

[1] logex [2] ex [3] x [4] x2

Q.65 A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the

position of the ball at 3T

second [AIEEE-2004]

[1] 18h17

meter from the ground [2] 9h7

meter from the ground

[3] 9h8

meter from the ground [4] 9h

meter from the ground

Q.66 The relation between time t and distance x is t = ax2 + bx where a and b are constants. The accelerationis - [AIEEE-2005]

[1] –2av3 [2] 2av2 [3] –2abv2 [4] 2bv3

Motion in one dimensionsQ.67 A car, starting from rest, accelerates at the rate f through a distance S then continues at constant speed for

time t and then decelerates at the rate 2f

to come to rest. If the total distance traversed is 15 S, then -

[1] S = 21

ft2 [2] S = 41

ft2 [3] S = 2ft2 [4] S = 61

ft2 [AIEEE-2005]

Q.68 A particle is moving eastwards with a velocity of 5 ms–1 . In 10 seconds the velocity changes to 5 ms–1 northwards.The average acceleration in this time is [AIEEE-2005]

[1] zero [2] 2ms

21

towards north-west

[3] 2ms

21

towards north-east [4] 2ms21 towards-north

Q.69 A bullet fired into a fixed target loses half of its velocity after penentarting 3 cm. How much further it will penetratebefore coming to rest assuming that if faces constant resistance to motion - [AIEEE-2005]

[1] 1.5 cm [2] 1.0 cm [3] 3.0 cm [4] 2.0 cm

Q.70 A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2m/s2. Hereaches the ground with a speed of 3m/s. At what height, did he bail out - [AIEEE-2005]

[1] 293 m [2] 111 m [3] 91 m [4] 182 m

Q.71 Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a directionperpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catchesthe other boy in a time t, where t is - [CPMT-2005]

[1] 21

2 vv/a [2] )vv(/a 1 [3] )vv/(a 21

22 [4] a/(v – v1)

Q.72 A ball is thrown vertically upward. It has a speed of 10m/sec when it has reached one half of its maximumheight. How high does the ball rise? Take g = 10 m/s2 - [CPMT-2005]

[1] 20 m [2] 15 m [3] 5 m [4] 10 m

Q.73 What will be the a vs x graph for the following graph? [IIT Scr.-2005]

[1] [2] [3] [4]


Q.74 A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies asv = a x . The displacement of the particle varies with time as - [AIEEE-2006]

[1] t [2] t1/2 [3] t3 [4] t2

Q.75 A car runs at a constant speed on a crcular track of radius 100m, taking 62.8 seconds for every circular lap.the average velocity and average speed for each circular lap respectively - [CPMT-2006]

[1] 0, 10 m/s [2] 10 m/s, 10 m/s [3] 10 m/s, 0 [4] 0, 0

Q.76 A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from Ois given by x = 40 + 12t – t3. How long would the particle travel before coming to rest. [CPMT-2006]

[1] 40m [2] 56m [3] 16m [4] 24m

Q.77 Two bodies, A(of mass 1kg) and B (of mass 3kg), are dropped from heights of 16m and 25m, respectively.The ratio of the time taken by them to reach the ground is [CPMT-2006]

[1] 12/5 [2] 5/12 [3] 4/5 [4] 5/4

Q.78 The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit time(t = 1) is [AIEEE-2007](1) v0 + g + f (2) v0 + g/2 + f (3) v0 + 2g + 3f (4) v0 + g/2 + f/ 3

Q.79 A particle moving along x-axis has acceleration f, at time t, given by 0tf f 1T

, where f0 and T are constants.

The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particlevelocity (vx) is [CPMT-2007]

(1) 01 V T2

(2) f0 T (3) 12

f0 T2 (4) f0 T

2

Q.80 A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speedfor this round trip is [CPMT-2007]

(1) u dv v2

(2) u d

d u

2v vv v (3) u dv v (4) u d

d u

v vv v

Q.81 The position x of a particle with respect to time t along x-axis is given by x = 9t2 – t3 where x is in metres andt in second, what will be the position of this particle when it achieves maximum speed along the +x direction.

[CPMT-2007](1) 24m (2) 32m (3) 54m (4) 81m

ANSWER KEY EXERCISE # 3Qus. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ans. 4 3 3 3 1 3 1 4 1 4 2 1 1 2 2Qus. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Ans. 3 2 2 3 4 4 2 2 3 1 2 3 2 2 3Qus. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45Ans. 2 3 2 4 3 3 2 2 2 1 3 1 2 4 1Qus. 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60Ans. 2 2 1 2 4 2 1 1 3 2 2 3 1 2 1Qus. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75Ans. 4 2 2 4 3 1 3 2 2 1 3 4 3 4 1Qus. 76 77 78 79 80 81Ans. 3 3 4 1 2 3

motion in one dimension exercise1

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