A force with magnitude $0.4t\,\text{N}$, acting at an angle of $30\degree$ above the horizontal, is applied to a particle $P$, where $t\,\text{s}$ is the time elapsed since the force begins to act. $P$ is stationary on rough horizontal ground when $t = 0$. The mass of $P$ is $0.2\,\text{kg}$ and the coefficient of friction between $P$ and the ground is $\mu$.
(i)[5]
Given that $P$ is on the point of slipping when $t = 2$, determine $\mu$ and the value of $t$ at the instant when $P$ loses contact with the ground.
(ii)[3]
While $P$ is moving on the ground, its velocity is $v\,\text{m s}^{-1}$ at time $t\,\text{s}$. Show that $\frac{dv}{dt} = 2.165t - 4.330$, where the coefficients are correct to 4 significant figures.
(iii)[4]
Calculate the speed of $P$ at the instant it loses contact with the ground.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “On resolving vertically, $R = 0.2g - 0.4\times2\sin30$” …