Question

A particle starts from rest with constant
acceleration. If first distance S is covered in time t,
then the time taken to cover next 28 distance is
(2) (root3 - 2)
(1) (root 2 - 1)
(3) (root3 - 1)
(4) 87​

Answer 1

Given :  A particle starts from rest with constant acceleration first distance S is covered in time t,

To find :  the time taken to cover next 2S distance

Solution:

u = 0  start from rest

a  = a  

t  = t

S = ut  + (1/2)at²

=> S = 0 + (1/2)at²

=>  a =  2S/t²

Time taken to cover next 2S

time taken for 3S   -    time taken for S

3S =  (1/2)at₃²

=>   t₃²  = 6S/a

=>  t₃²  = 6S/(2S/t²)

=> t₃² = 3t²

=>  t₃ = √3 t

time taken for 3S =  √3 t

Time taken to cover next 2S  = √3 t - t= (√3 - 1 ) t

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