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

s = 2t³ − t⁴ + 5t² + ct + d

where $c$ and $d$ are constants.