1. The motion of a particle is modelled as having constant acceleration $am{s}^{-2}$, initial velocity $um{s}^{-1}$ and final velocity $vm{s}^{-1}$ such that at time $t$ seconds

$v=u+at$

Use integration to show that the displacement, $s$ m, of the particle from its initial position is given by

$s=ut+\frac{1}{2}a{t}^{2}$