Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A tiny object with mass $0.2\,\text{kg}$ is initially at rest at point $O$ on a rough horizontal surface. The coefficient of friction between the object and the surface is $0.5$. A force of magnitude $P\,\text{N}$ acting at an angle $\theta$ below the horizontal is applied to the object. At time $t\,\text{s}$ after the force starts to act, the object's velocity is $v\,\text{m s}^{-1}$ away from $O$ (see diagram). It is given that $\tan\theta = \frac{3}{4}$ and that $P = 0.4t$ for $0 \leq t \leq 8$.
(i)[3]
Find the value of $t$ at which the object starts to move.
(ii)[2]
Show that, while the force is acting and the object is moving, $\frac{dv}{dt} = t - 5$.
(iii)[5]
At $t = 8$ the force of magnitude $P\text{ N}$ stops acting. Find the distance the object travels after $t = 8$ before it comes to rest.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtains $R = 0.2g + 0.4t\sin \theta = 2 + 0.24t$ and $F = 0.5(2 + 0.24t)$” …