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

a = f
`(dv)/(dt)=fimpliesunderset(u)overset(v)intdv=underset(o)overset(t)intf dt =impliesv = u +ft`
`v = (dx)/(dt)=u+ftimpliesunderset(0)overset(100)intdx=underset(t-1)overset(t+1)int(u+ft)dt`
`implies2u +2f t=100 implies u+ft = 50" "......(1)`
at t sec implies `v = u + ft = 50 cm//s` by (1)