By Team Aakash Byju's | 28th December 2022

How to Find the Average Velocity at Different Time Intervals?

The position versus time graph for a certain particle moving along the x-axis is shown in the figure.

C

A

B

Find the average velocity in the time intervals

0 to 2s

2s to 4s

4s to 7s

Detailed Explanation

The correct answers are V       for 0 to 2s is 5 m/s  V       for 2 to 4s is −2.5 m/s  V       for 4 to 7s is −3.3 m/s 

Arrow

avg

avg

avg

In the given position-time graph, the slope is the displacement divided by the time interval of that displacement which indeed is an average velocity.

If x   and x   are the initial & final positions and t  & t   are the initial & final times, then the average velocity is

1

2

1

2

v     =

av

x  - x

t  - t

2

2

1

1

For (a) where t  = 0s, t  = 2s, from the image it is noted that x  = 0 m &  x   = 10 m

v     =

av

10 - 0

2 - 0

=  5 m/s

1

2

1

2

Use the same method for (b) and (c)

1

2

(b) t  = 2s, t   = 4s, x  = 10 m &  x  = 5 m

2

v     =

av

5 - 10

4 - 2

= -2.5 m/s

1

(c) t  = 4s, t  = 7s, x  = 5 m &  x   = −5 m

2

1

2

v     =

av

-5 - 5

7 - 4

= -3.3 m/s

1

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