1.3: Velocity, acceleration and displacement

A particle $\displaystyle P$ is moving along a straight line which passes through the fixed point $\displaystyle O$. At time $\displaystyle t$ seconds, $\displaystyle t\geq0$, the velocity, $\displaystyle v\,\mathrm{m\,s^{-1}}$, of $\displaystyle P$ is given by

At time $\displaystyle t$ seconds the acceleration of $\displaystyle P$ is $\displaystyle a\,\mathrm{m\,s^{-2}}$.

(a) Find an expression for $\displaystyle a$ in terms of $\displaystyle t$.

The displacement of $\displaystyle P$ from $\displaystyle O$ is $\displaystyle 7\,\mathrm{m}$ when $\displaystyle t=2$.

(b) Find the exact displacement of $\displaystyle P$ from $\displaystyle O$ when $\displaystyle t=4$.