A body moves from rest from a point A. It moves to another point B in 10s, the motion being accelerated one and achieves a velocity 60 m/s at B. It then moves on to C with uniform velocity for 20 s when it is immediately brought to rest. Draw a graph showing complete motion and calculate the total distance travelled.

Expert Answers

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The body starts from rest at point A and accelerates uniformly for 10 s until it reaches B, at which point its velocity is 60 m/s. Thus, the body accelerates uniformly from 0 m/s to 60 m/s in 10 s. Then the body moves with a uniform velocity of 60 m/s for next 20 s and then stops abruptly.

The distance traveled by the body can be divided into 2 different intervals: first 10 s (when it accelerates) and next 20 s (when it is undergoing uniform motion).

Average velocity for first 10 s: 1/2 (velocity at A + velocity at B)

= 1/2 (0 + 60) m/s = 30 m/s

Distance traveled for 10 s at an average speed of 30 m/s

= 10 s x 30 m/s = 300 m

From B to C: distance traveled = speed x time

= 60 m/s x 20 s = 1200 m.

Thus, total distance traveled = distance from A to B + distance from B to C

= 300 m + 1200 m 

= 1500 m.

See the attached velocity-time plot.

Hope this helps. 

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