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. (a) `20`
B. (b) 30`
C. (c ) ` 50 `
D. (d) ` 80`

Answer

C

Explanation

Given , ` 100 = D_1 + D_(1-1)`
` `= [ u + f/2 (2t-1) ] + [u +f/2 {2 (t+1}]`
or ` 100 =2 u + f/2 (4 t) = 2 u + 2 ft` or ` 50 =u + ft`
Velocity after (t) seconds, ` v= u + ft 50 cm//s`.