Variable acceleration (calculus in kinematics)

A particle $P$ moves along a straight line. At time $t$ seconds, the acceleration of $P$ is $(4-2t)\ \mathrm{m\,s^{-2}}$. When $t=0$, $P$ is at the point $O$ and has velocity $3\ \mathrm{m\,s^{-1}}$.

(a) Find the velocity of $P$ when $t=2$. [3]

(b) Find the displacement of $P$ from $O$ when $t=3$. [2]

A particle $P$ moves along a straight line. At time $t$ seconds, $t\ge0$, the velocity of $P$ is $v\ \mathrm{m\,s^{-1}}$, where $$v=3t^2-12t+9$$

(a) Find the values of $t$ when $P$ is instantaneously at rest. [2]

(b) Find the acceleration of $P$ when $t=4$. [2]

(c) Find the total distance travelled by $P$ in the interval $0\le t\le 3$. [3]