CBSE Class 12-science Answered

If the block starts from rest and sliding along the inclined plane ,

then the distance d moved by block at time t is

d = (1/2) a t²  

Let us divide time interval of 1 s time dur ation  .

Distance d_n moved after n seconds is ,  d_n = (1/2) a n²

Distance d_n-1 moved after (n-1) seconds is ,  d_n-1 = (1/2) a (n-1)²

Distance d_n-2 moved after (n-2) seconds is ,  d_n-2 = (1/2) a (n-2)²

Let S_n be the time travelled between (n-1) s and (n+1) s

S_n = ( d_n - d_n-1 ) = (1/2) a [ n² - (n-1)² ] = (1/2) a [ 2n-1 ]

Let S_n-1 be the time travelled between (n-2) s and (n-1) s

S_n-1 = ( d_n-1 - d_n-2 ) = (1/2) a [ (n-1)² - (n-2)² ] = (1/2) a [ 2n-3 ]