Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

Particle $P$ has mass $0.5\,\text{kg}$ and is initially at rest at the point $O$ on a rough horizontal surface. At $t = 0$, where $t$ is measured in seconds, a horizontal force in a fixed direction begins to act on $P$. At time $t$ the force has magnitude $0.6t^2\,\text{N}$ and the velocity of $P$ away from $O$ is $v\,\text{m s}^{-1}$. 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 then show that $\frac{dv}{dt} = 1.2t^2 - 0.3$ for $t > 0.5$.

(ii)[3]

Express $v$ in terms 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.

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI