Kinematics

KINEMATICS

STATICS is the study of the motion of an object under the effect of forces in equilibrium…

KINEMATICS is the study of the motion of the objects without taking into account the cause of their motion...

DYNAMICS is the study of the motion of the objects by taking into account the cause of their motion...

introduction

POSITION-TIME GRAPH (UNIFORM MOTION)

Position-time graph for an object in uniform motion along a straight path is a straight line inclined to the time axis...

The velocity of uniform motion is equal to the slope of position-time graph...

PO

SIT

ION

(m)

TIME(s)

VELOCITY-TIME GRAPH (UNIFORM MOTION)

Displacement of an object in time interval is numerically equal to the area under velocity-time graph between the instants...

velo

city

time

UNIFORMLY ACCELERATED MOTIONIN A STRAIGHT LINE

The motion of an object is said to be uniformly accelerated ,if the same change in its velocity takes place in each unit of time…

Average speed is defined as the ratio of the path length to the time taken by the object to cover that path…

AVERAGE SPEED OF UNIFORM MOTION=(Path length)/(time interval)…

Average velocity is defined as the ratio of the displacement to the time taken by the object to cover that displacement….

AVERAGE VELOCITY OF THE UNIFORM MOTION = (Displacement)/(time interval).

The average velocity of an object is a vector quantity.

Rest And Motion

An object is said to be in motion , if it changes its position with respect to its surroundings with the passage of time.

EXAMPLES:-

An airplane or a bird flying through the air A ball thrown by a girlA ship sailing on a sea

If the object doesn’t change its position with respect to its surroundings with the passage of time, it is said to be at rest.

Sometimes the objects are in motion but the motion may not be visible to us.

For example , a gas molecules are always in ceaseless random motion , though their motion is not visible to the naked eye.

UNIFORM MOTION IN A STRAIGHT LINE

UNIFORM MOTION:- The motion of an object is said to be uniform, if it covers equal displacements in equal interval of time.

UNIFORM SPEED:- It is defined as the ratio of the path length to the time taken by the object to cover that path.

Speed of the uniform motion = (path length)/(time interval)

UNIFORM VELOCITY:-It is defined as the ratio of displacement to the time taken by the object to cover that displacement.

Velocity of the uniform motion =(displacement)/(time interval)

O A

B X

X’

X

AT t=0 AT t=t AT t=t’

V=(x’-x)/(t’-t)

EXPRESSION FOR DISPLACEMENT

V=(x’-x)/(t’-t)

x’-x=v(t’-t)

x’=x + v(t’-t)

XO A B

xo

x

x = x0 +v(t’-0)

x = xo + vt

x – x0 =vtIf x-xo=S, the displacement of the object in time t, then the equation becomes S=vt

AT t=0 AT t=t

Velocity Time Relation

a = acceleration due to gravitya = (v’-v)/(t’-t)

v’ = v + a(t’-t)

This equation is velocity time relation, which gives the velocity of an object at any time t and

the uniform acceleration a of the object.

a = (v-u)/(t-0) =(v-u)/t

v =u + at

Questions1. A body travels from A to B at 40m/s and from B to A at

60m/s. Calculate the average speed and average velocity?

Ans:- let t1 and t2 be time in seconds taken by the body to go from A to B and then from B to A respectively. Then,

t1 + t2 = AB/40 + BA/60= AB(1/40 +1/60)

= AB/24s

Total distance covered = AB + BA = 2ABAverage speed = 2AB/t1+t2

=2AB /AB/24= 48m/s

Since the body reaches the starting position, the net displacement is o. Therefore,

Average velocity = displacement/time=0/AB/24 = 0

POSITION-TIME GRAPH FOR TWO OBJECTS MOVING WITH EQUAL

VELOCITIES

Posi

tion

(m)

Time(s)

For object P’

For object P

Thus position time graph for 2 objects P and P’ moving with equal velocity along a straight path will be the two parallel lines.

POSITION TIME GRAPH FOR TWO OBJECTS MOVING WITH

UNEQUAL VELOCITIES

For object P

For object P’

Position of meeting

Time of meeting

posi

tion

time

Thus, if 2 objects move with unequal velocities ,then the position time graph will be straight lines inclined to time axis and intersect each other.

If the velocities of the 2 objects are of opposite signs, then the magnitude of their relative velocity v’-v is greater than the magnitudes of both v and v’.

Tha

nk

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