A particle is moving in a straight line with initial velocity `u` and uniform acceleration `f`. If the sum of the distances travelled in `t^(th) and (t + 1)^(th)` seconds is `100 cm`, then its velocity after `t` seconds, in `cm//s`, is.

Options

A. 20
B. 30
C. 50
D. 80

Answer

C

Explanation

Distance travelled in `t^(th)` second of uniformlly accelerated motion is
`s_1 = u + a/2 (2t-1)" "…(i)`
Distance travelled in `(t+1)^(th)` second can be written as `S_(t+1) = u + a/2 (t+1) - 1`
or `S_(t+1) = U + a/2 (2t+1) " "…(ii)`
`s_1 + s_(t+1) =100 cm ` (given)
`u + a/2 (2t -1) + u + a/2 (2t+1) = 100 " "`[Using (i) and (ii)]
or 2u + 2at = 100 or u + at = 50 , `therefore v = 50 cm s^(-1)`