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Question

The following plot shows the velocity-time relation of a moving body.
Then, pick the CORRECT statement(s) from the following.
  1. The body decelerated at a rate of 5 m s2 in the last two seconds of its motion.
  2. The body has uniformly accelerated motion for a total of 6 s.
  3. The body is displaced by 62.5 cm.
  4. The body accelerated at a rate of 5 m s2 in the first four seconds of its motion.


Solution

The correct options are
A The body decelerated at a rate of 5 m s2 in the last two seconds of its motion.
B The body has uniformly accelerated motion for a total of 6 s.
C The body is displaced by 62.5 cm.
The slope of velocity-time graph of a body gives the acceleration of the body. 
Acceleration from time (t) = 3 s to t=4 s is 10543=5 m s2
The body is accelerating from t=3 s to t=4 s, i.e. for one second.
And, acceleration from time (t) = 7 s to t=9 s is 01097=5 m s2
An increasing slope indicates that the body is accelerating, while a decreasing one indicates deceleration.

Also, from t=0 s to t=3 s, and from t=4 s to t=7 s, the slope is constant which indicates that the body has uniform velocity, i.e. acceleration of the body is zero for about 6 s.
The area under the velocity-time graph gives the total (net) displacement of the body:
The sum of the areas of the sections A to E gives the net displacement.

Net displacement = 15 cm+5 cm+2.5 cm+30 cm+10 cm=62.5 cm

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