Standard +0.3 This is a straightforward mechanics question requiring differentiation to find velocity, solving a cubic equation (which factorises nicely), and calculating distance between two positions. While it involves multiple steps, each is standard A-level technique with no novel insight required, making it slightly easier than average.
A particle \(P\) moves in a straight line. At time \(t\) s the displacement \(s\) cm from a fixed point \(O\) is given by:
$$s = \frac{1}{6}\left(8t^3 - 105t^2 + 144t + 540\right).$$
Find the distance between the points at which the particle is instantaneously at rest. [7]
A particle $P$ moves in a straight line. At time $t$ s the displacement $s$ cm from a fixed point $O$ is given by:
$$s = \frac{1}{6}\left(8t^3 - 105t^2 + 144t + 540\right).$$
Find the distance between the points at which the particle is instantaneously at rest. [7]
\hfill \mbox{\textit{SPS SPS FM Mechanics 2021 Q2 [7]}}