A body at rest starts sliding from top of a smooth inclined plane and requires 4 seconds to reach bottom. How much time does it take, starting from rest at top, to cover one-fourth of a distance?

Question

i) 1 ii) 2 iii) 3 iv) 4

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Answer 1 · 2017-06-01T04:49:40

Let the length of the inclined plane be #L# and the acceleration of the body during its sliding is #a# .The initial velocity being #u=0#

The time of sliding of # L# length is 4s,
So #L=0xx4+1/2xxaxx4^2#

#=>L=8a......[1]#

Let the time of sliding of # L/4# length from the top, starting from rest be t s,

So #L/4=0xxt+1/2at^2#

#L/4=1/2at^2.....[2]#

Comparing [1] and[2]

#(8a)/4=1/2at^2#

#=>t^2=4#

#=>t=2#s