What is velocity-time graph? Sate how it can be used to find:

i. acceleration of a body

ii. the displacement of a body, and

iii. the distance travelled in a given time

The Velocity – Time graph gives the change of velocity with the change in time.

Y – Axis : Velocity

X – Axis : Time

Now, slope of velocity – time graph is gives as

Slope = =

Since, y = v (Velocity)

And x = t (Time)

Now, there are three types of Velocity – Time graph.

a) Velocity is constant – Uniform Motion

This means that velocity remains same for all time.

b) Uniformly Accelerated Motion

This means that velocity changes at constant rate.

Slope = Constant and the graph is a straight line graph

c) Non – Uniformly Accelerated Motion

This means that velocity changes at a variable rate.

Slope = Variable and the graph is as shown below

Velocity – Time Graph can be used to find the following as:

a) Acceleration:

Slope of Velocity – Time Graph = Acceleration

Since, Slope =

So, Acceleration =

And hence, Slope = Acceleration

b) Displacement of a body:

The area under the velocity – time graph gives the displacement of the body.

Displacement = Velocity × Time

Area under the graph = Displacement of Body

For finding the area, we multiply the velocity and time.

c) Distance of a body:

Distance = Speed × Time

Now, Speed is magnitude of velocity.

Hence, as long as velocity is positive,

Area under the curve = Distance

NOTE:

If velocity is negative, then the area under the curve is negative and then the total area gives displacement. So, in that case,

Distance Displacement

Example:

Let the velocity – time graph be as shown below:

Now, Displacement = Area under the curve

=

= 5 m

Whereas, Distance =

= 15 m

For displacement we have considered the area below the time axis as negative whereas for distance, we have considered all areas as positive.