Particle $P$, with mass $0.4\,\text{kg}$, is let go from rest at point $O$ on a smooth plane that is inclined at $30^\circ$ to the horizontal. A force of magnitude $3e^{-t}\,\text{N}$, acting up the line of greatest slope, is applied to $P$, where $t$ is the time after release.
(i)[2]
Hence show that $\frac{dv}{dt} = 7.5e^{-t} - 5$, where $v\,\text{m s}^{-1}$ denotes the velocity of $P$ up the plane at time $t\,\text{s}$.
(ii)[3]
Express $v$ as a function of $t$.
(iii)[3]
Find the distance of $P$ from $O$ when $v$ reaches its maximum value.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Writes $0.4\,\frac{dv}{dt} = 3e^{-t} - 0.4g\sin30$” …