The acceleration of a particle varies with time t seconds according to the relation `a=6t+6ms^-2`. Find velocity and position as funcitons of time. It is given that the particle starts from origin at `t=0` with velocity `2ms^-1`.

Explanation

We know that `intdv=int adtimpliesint_2^vdv=int_0^t(6t+6)dt`
`impliesv-2=[(6t^2)/(2)+6t]_0^timpliesv=3t^2+6t+2`
Now `intdx=intvdtimpliesint_0^xdx=int_0^t(3t^2+6t+2)dt`
`implies x=t^3+3t^2+2t`