Question

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

Solution

## The correct options are A The body decelerated at a rate of 5 m s−2 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 10−54−3=5 m s−2 ⟹ 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 0−109−7=−5 m s−2 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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