The acceleration of a'particle starting from rest, varies with time according to the relation `a=kt+c`. The velocity of the particle after time `t` will be :

Options

A. `(alpha t^(2))/(2) + beta`
B. `(alpha t^(2))/(2) + beta t`
C. `alpha t^(2) + (1)/(2) beta t`
D. `((alpha t^(2) + beta))/(2)`

Answer

B

Explanation

`a = alpha t + beta`
`(dv)/(dt) = alpha t + beta`
`v = (alpha t^(2))/(2) + beta t`