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A car starts moving along a line, first with acceleration $a = 5 {ms}^{- 2}$ starting from rest, then uniformly and finally decelerating at the same rate a and comes to rest. The total time of motion is 25 s. The average speed during the time is $20 {ms}^{- 1}$ . How long does particle move uniformly?

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10 s

12 s

20 s

15 s

answer is D.

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Detailed Solution

Average velocity $= \frac{Total displacement}{Total time}$

or $20 = \frac{\frac{1}{2} \times a \times t^{2} + (a t) (25 - 2 t) + \frac{1}{2} \times a \times t^{2}}{25}$

Solving this equation with $a = 5 {ms}^{- 2}$ , we get
t = 5s
Thus, the particle moved uniformly for (25 - 2 t) or 15 s.

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