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) = f " " rArr underset(u) overset(v)int dv = underset(0) overset(t) int fdt`
`rArr v = u + ft`
`v = (dx)/(dt) = u + ft`
`rArr underset(0) overset(100)int dx = underset(t - 1)overset(t + 1)int (u + ft) dt rArr 2u + 2f t`
`= 100 rArr u + ft = 50` ....(1)
`v t sec rArr v = u + ft = 50 cm//s` by (1)