In this question, all lengths are in metres and time is in seconds.
A particle \(P\) moves in a straight line such that its displacement \(s\) from a fixed point \(O\) at time \(t\) is given by \(s=(t-4)^2(t-1)\) for \(t\ge0\).
On the axes, sketch the displacement–time graph of \(P\), stating the intercepts with the axes.[2]
Find an expression for the velocity, \(v\), of \(P\).
Give your answer in a factorised form.[2]
On the axes, sketch the velocity–time graph of \(P\), stating the intercepts with the axes.[2]
Find an expression for the acceleration, \(a\), of \(P\).[1]
On the axes, sketch the acceleration–time graph of \(P\), stating the intercepts with the axes.[3]