1. A particle is moving in a straight line and at time $t$ seconds has acceleration, $am{s}^{-2}$, where $a=12t−12{t}^{2}+10$.

Show that the displacement, $s$ m, of the particle from a fixed point $O$ , is given by

$s=2{t}^{3}-{t}^{4}+5{t}^{2}+ct+d$

where $c$ and $d$ are constants.