3.119: Velocity–time graph and related particle

In this question all distances are in metres and all times are in seconds.

The diagram shows the velocity–time ($v$–$t$) graph of a particle travelling in a straight line. The particle travels a distance of $2750\,\mathrm{m}$ in $120\,\mathrm{s}$. Find the velocity, $V$, of the particle when $t=70$.

Find the acceleration of the particle for $70\leqslant t\leqslant 120$.

A different particle moves in a straight line such that its velocity, $v\,\mathrm{ms}^{-1}$, $t$ seconds after leaving a fixed point $O$, is given by $v=\left(t^{2}+\dfrac{1}{2}\right)^{5}$.

Find the exact acceleration of the particle when $t=2$.

Explain why the particle does not change direction for $0\leqslant t\leqslant 2$.