1.61: Particle Motion from Velocity

A particle $\displaystyle P$ moves in a straight line. At time $\displaystyle t$ seconds, the velocity $\displaystyle v\,\mathrm{m}/\mathrm{s}$ of $\displaystyle P$ is given by

(a) Find the acceleration of $\displaystyle P$, in $\displaystyle \mathrm{m}/\mathrm{s}^2$, when $\displaystyle t=3$.

(b) Find the distance, in $\displaystyle \mathrm{m}$, that $\displaystyle P$ travels in the interval $\displaystyle 0\leqslant t\leqslant6$.