Question

Figure shows the displacement of a body at different times. (a) Calculate the velocity of the body as it moves for time interval (i) 0 to 5 s, (ii) 5 s to 7 s and (iii) 7 s to 9 s. (b) Calculate the average velocity during the time interval 5 s to 9 s. [ Hint — From 5 s to 9 s, displacement = 7 m – 3 m = 4 m ]

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Answer

Below is the displacement-time graph of the body with the different points marked:

body-displacement-different-times

(a) As we know,

(i) At t = 0 to 5 s

Velocity = Slope of straight line OA

Velocity = AE \over OE

= 3 - 0 \over 5 - 0

= 3 \over 5

= 0.6 m s-1

Hence, velocity at t = 0 to 5 s = 0.6 m s-1

(ii) At t = 5 to 7 s

In this part, we observe that there is no change in the Y axis, (i.e. displacement is zero so the body is stationary).

Hence, velocity at t = 5 to 7 s = 0 m s-1

(iii) At t = 7 s to 9 s

Velocity = Slope of straight line BC

Velocity = CD \over BD

= 7 - 3 \over 9 - 7

= 4 \over 2 = 2 m s-1

(b) As we know,

Average velocity = 7 - 3 \over 9 - 5

= 4 \over 4 = 1 ms-1

Hence, average velocity of the car is 1 ms-1.

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