A particle $P$ with mass $0.2\,\text{kg}$ is projected horizontally at velocity $0.9\,\text{m s}^{-1}$ from point $O$ on a rough horizontal surface. $P$ travels in a straight line, and at time $t\,\text{s}$ after projection its velocity is $v\,\text{m s}^{-1}$. A force of magnitude $0.024t\,\text{N}$ acts on $P$ in the direction $OP$. The coefficient of friction between $P$ and the surface is $0.3$.
(i)[4]
Write the acceleration of $P$ in terms of $t$, and hence show that, before $P$ is brought to rest, $v = 0.06(t^2 - 50t + 15)$.
(ii)[2]
Determine the value of $t$ at which $P$ comes to rest.
(iii)[2]
Determine the value of $t$ when $P$ later begins to move again.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Newton's second law is used: $0.2a = 0.024t - 0.2g \times 0.3$” …