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A particle moving in a straight line with uniform retardation described 7cm in 5th second and after some time comes to rest. If the particle describes 1/64 part of the total path during the last second of its motion, for how long was the particle in motion?

A particle moving in a straight line with uniform retardation described 7cm in 5th second and after some time comes to rest. If the particle describes 1/64 part of the total path during the last second of its motion, for how long was the particle in motion? Correct Answer 8 seconds

Let the initial velocity of the particle be u cm/second and its uniform retardation be f cm/sec2. Further assume that the particle was in motion for t seconds. By question, the particle comes to rest after t seconds. Therefore, using the formula, v = u – ft, we get, 0 = u – ft Or u = ft Again, the particle described 7cm in the 5th second. Therefore, using the formula st = ut + 1/2(f)(2t – 1) we get, 7 = u – ½(f)(2.5 – 1) Or u – 9f/2 = 7 Again, the distance described in the last second (i.e., in the t th second) of its motion = 1/64 * (distance described by the particle in t seconds) ut -1/2(f)(2t – 1) = 1/64(ut – ½(ft2)) Putting u = ft, we get, f/2 = 1/64((ft2)/2) Or t2 = 64 Or t = 8 seconds.

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