1.21: A particle is moving along the -axis.

A particle $\displaystyle P$ is moving along the $\displaystyle x$-axis. At time $\displaystyle t$ seconds, $\displaystyle t \geq 0$, the velocity, $\displaystyle v \mathrm{m}/\mathrm{s}$, of $\displaystyle P$ is given by $\displaystyle v = 2t^2 - 16t + 30$

(a) Find the acceleration, in $\displaystyle \mathrm{m}/\mathrm{s}^2$, of $\displaystyle P$ when $\displaystyle t = 5$

$\displaystyle P$ comes to instantaneous rest at the points $\displaystyle M$ and $\displaystyle N$ at times $\displaystyle t_1$ seconds and $\displaystyle t_2$ seconds where $\displaystyle t_2 > t_1$

(b) Find the exact distance $\displaystyle MN$