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?

Category: QuestionsA 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?
Editor">Editor Staff asked 11 months ago

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) 6 seconds
 
(b) 8 seconds
 
(c) 4 seconds
 
(d) 2 seconds
 
I got this question in examination.
 
This interesting question is from Calculus Application topic in chapter Application of Calculus of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct answer is (b) 8 seconds
 
Explanation: Let the initial velocity of the particle be u cm/second and its uniform retardation be f cm/sec^2.
 
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(ft^2))
 
Putting u = ft, we get,
 
f/2 = 1/64((ft^2)/2)
 
Or t^2 = 64
 
Or t = 8 seconds.