1.44: A particle moves in a straight line.

A particle $\displaystyle P$ moves in a straight line. At time $\displaystyle t$ seconds, the velocity, $\displaystyle v$$\displaystyle \mathrm{m}/\mathrm{s}$, of $\displaystyle P$ is given by

(a) Show that $\displaystyle P$ never comes to rest.

(b) Find the acceleration of $\displaystyle P$, in $\displaystyle \mathrm{m}/\mathrm{s}^{2}$, when $\displaystyle t = 4$

Using algebra

(c) find the distance, in m, that $\displaystyle P$ travels in the interval $\displaystyle 0 \leq t \leq 5$