1.5: Displacement, velocity and acceleration

A particle $\displaystyle P$ moves along the $\displaystyle x$-axis. At time $\displaystyle t$ seconds, the displacement, $\displaystyle x$ metres, of $\displaystyle P$ from the origin $\displaystyle O$ is given by

(a) Find the velocity, in $\displaystyle \mathrm{m\,s^{-1}}$, of $\displaystyle P$ when $\displaystyle t=3$.

(b) Find the value of $\displaystyle t$ for which $\displaystyle P$ is instantaneously at rest.

(c) Find the acceleration, in $\displaystyle \mathrm{m\,s^{-2}}$, of $\displaystyle P$ when $\displaystyle t=2$.