Motion along a straight line

Standard 9

Person outside the bus

The bus moved away from the tree

The person is comparing the position of the bus with respect to the position of the tree

Reference (or origin) is position of the tree

0 5 10

Person inside the bus

The tree moved away from the bus.

The person is comparing the position of the tree with respect to the position of the bus.

Reference (or origin) is position of the bus.

0510

Motion is relative

Both the observations are correct. The difference is what is taken as the origin.

Motion is always relative. When one says that a object is moving, he/she is comparing the position of that object with another object.

Motion is therefore change in position of an object with respect to another object over time.

Kinematics studies motion without delving into what caused the motion.

Direct Path (1.1 km)Actual Path (2 km)

Q. How much distance do you have to travel to reach school?

Q. If you were to draw a straight line between your house and school, what would be the length of that line?

Direct Path (1.1 km)Actual Path (2 km)

Q. How much distance do you travel in one round trip to the school?

Q. After one trip how far away are you from your home?

Distance and Displacement

Distance = length of the actual path taken to go from source to destination

Displacement = length of the straight line joining the source to the destination or in other words the length of the shortest path

CheckpointSuppose it was given that the person started by point A and walked in a straight line for 5 km. Can you calculate the end point of his/her journey?

A

No, the person could be anywhere on the circle of 5 km radius.

Unless we know the direction of the motion we cannot calculate the end point of the journey.

Sample ProblemRohit and Seema both start from their house. Rohit walks 2 km to the east while Seema walk 1 km to the west and then turns back and walks 1 km.

Distance travelled by them is the same (2 km)

Is their displacement also the same?

No – Seema is back home and her displacement is 0 m.

This is because direction of motion is different in both cases.

You require both distance and direction to determine displacement.

Sample Problem

A B

CDistance AB = 3 km due EastDistance BC = 4 km due North What is the distance travelled by a person who moves from A to C via B? What is the displacement? What is the direction of the displacement?

Distance travelled = 7 km, Displacement = 5 km from A towards C.

Rate of Motion

Distance travelled per unit time or the displacement per unit time.

When an object is travelling along a straight line its velocity is equal to its speed.

Sample Problem

r = 100 m

Distance = = 6280 m, Displacement = 0 m

Speed = = = 180 km/hr

The adjoining figure shows a Formula 1 racing track. A driver is did 10 laps, what is the distance travelled by the driver at the end of the race?

What is the displacement?

If the driver took 125.6 seconds to complete the laps, what is his speed and velocity in km/hr?

Uniform Motion

A distance – time graph represents the distance travelled with respect to time.

When an object covers equal distance in every time interval, it is said to be having uniform motion.

In an uniform motion, the speed of the object remains constant.

A stationary body is also an example of uniform motion

25

20

15

10

5

010 20 30 40 500

Dist

ance

(m)

Time (s)

Distance – Time graph

1.25

1.0

0.75

0.5

0.25

010 20 30 40 500

Spee

d (m

)/s

Time (s)

Speed – Time graph

Area of shaded region = 0.5 * 40 = 20mDistance travelled = 20 m

Velocity – Time graph25

20

15

10

5

010 20 30 40 500

Dist

ance

(m)

Time (s)

Distance – Time graph

1.25

1.0

0.75

0.5

0.25

010 20 30 40 500

Velo

city

(m)/

s

Time (s)

Velocity – Time graphUniform Motion

Acceleration = 0 m/s2

1.25

1.0

0.75

0.5

0.25

010 20 30 40 500

Velo

city

(m)/

s

Time (s)

Velocity – Time graphNon-uniform Motion

Acceleration = 0.125 m/s2

Uniform and Non-Uniform Motion

Rate of Change of Velocity

Rate of change of velocity

acceleration = meter/second2

A body is said to be accelerating if there is a change in velocity.

Velocity has magnitude and direction. A body has acceleration when either of them changes.

1.25

1.0

0.75

0.5

0.25

010 20 30 40 500

Velo

city

(m)/

s

Time (s)

Velocity – Time graphUniform Acceleration

Acceleration = 0.125 m/s2

1.25

1.0

0.75

0.5

0.25

010 20 30 40 500

Velo

city

(m)/

s

Time (s)

Velocity – Time graphNon-uniform Acceleration

Uniform and Non-Uniform Acceleration

Sample Problem25

20

15

10

5

010 20 30 40 500

Velo

city

(m/s

)

Time (s)

A

B

C

D

Which object has the maximum acceleration?

Which object has no acceleration?

How much distance is covered by object D in 20 seconds?

Explain the motion represented by D. Given an example of such a motion in real life.

1st Equation of Motionv

u

0t0

Velo

city

(m)/

s

Time (s)

Velocity – Time graphUniform Acceleration

Initial velocity = uFinal velocity = vTime = tAcceleration = aDisplacement = s

Acceleration = Rate of change of velocity

2nd Equation of Motionv

u

0t0

Velo

city

(m)/

s

Time (s)

Velocity – Time graphUniform Acceleration

Initial velocity = uFinal velocity = vTime = tAcceleration = aDisplacement = s

Displacement = Area under the line

But or

3rd Equation of Motionv

u

0t0

Velo

city

(m)/

s

Time (s)

Velocity – Time graphUniform Acceleration

Initial velocity = uFinal velocity = vTime = tAcceleration = aDisplacement = s

Displacement = Area under the line

But t