Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ has mass $0.5\,\text{kg}$ and is initially at rest at a point $O$ on a rough horizontal surface. At time $t = 0$, where $t$ is measured in seconds, a horizontal force acting in a fixed direction is applied to $P$. When the time is $t$ s, the force has magnitude $0.6t^2\,\text{N}$ and the velocity of $P$ away from $O$ is $v\,\text{ms}^{-1}$. It is stated that $P$ stays at rest at $O$ until $t = 0.5$.
(i)[3]
Calculate the coefficient of friction between $P$ and the surface, and show that $\frac{dv}{dt} = 1.2t^2 - 0.3$ for $t > 0.5$.
(ii)[3]
Express $v$ as a function of $t$ for $t > 0.5$.
(iii)[3]
Find the displacement of $P$ from $O$ when $t = 1.2$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme.