1.65: Particle Motion from Acceleration

A particle $\displaystyle P$ is moving along the $\displaystyle x$-axis. At time $\displaystyle t$ seconds, $\displaystyle t\geqslant0$, the acceleration of $\displaystyle P$ is $\displaystyle a\,\mathrm{m}/\mathrm{s}^2$, where

When $\displaystyle t=0$, $\displaystyle P$ is at rest at the origin $\displaystyle O$.

(a) Find the velocity of $\displaystyle P$ when $\displaystyle t=2$.

At time $\displaystyle t=T$, where $\displaystyle T>0$, $\displaystyle P$ is instantaneously at rest.

(b) Find the value of $\displaystyle T$.

(c) Find the total distance travelled by $\displaystyle P$ during the first 8 seconds of its motion.