If `a=(3t^2+2t+1)` `m/s^2` is the expression according to which the acceleration of a particle varies. Then-
`a=(3t^2+2t+1)` `(m)/(s^2)`
Q. The expression for instantaneous velocity at any time `t` will be (if the particle was initially at rest)-

Options

A. `t^3+2t+1`
B. `t^3+t+1`
C. `t^3+t^2+1`
D. `t^3+t^2+t+C`

Answer

C

Explanation

`a=3t^(2)+2t+1`
`int_(0)^(t)dv=int_(0)^(t)3t^(2)+2t+1)dt`
`v=t^(3)+t^(2)+t`