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 \(t=70\).[2]
Find the acceleration of the particle for \(70<t<120\).[2]
A different particle moves in a straight line such that its velocity, \(v\,\mathrm{m\,s}^{-1}\), \(t\) seconds after leaving a fixed point \(O\), is given by \(v=t(t^2+5)^{\frac12}\).
Find the exact acceleration of the particle when \(t=2\).[4]
Explain why the particle does not change direction for \(t>0\).[1]