The intial velocity of a particle is u (at t=0) and the acceleration is given by f=at. Which of the following relations is valid ?

Options

A. `v=u+at^(2)`
B. `v=u+(at^(2))/(2)`
C. `v=u+at`
D. v=u

Answer

B

Explanation

as f=at
`(dv)/(dt)=at rArr int_(u)^(v)dv=int_(0)^(f)`at dt
`(v-u)=(at^(2))/(2) rArr v=u+(1)/(2)at^(2)`