| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2021 |
| Session | November |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | Constant acceleration vector problems |
| Difficulty | Standard +0.8 This is a multi-part mechanics question requiring vector force analysis, integration to find velocity and position, and solving for specific conditions. Part (a) is straightforward equilibrium. Part (b) requires finding when velocity has zero i-component (integration and solving a cubic equation). Part (c) needs double integration of forces to find displacement. The variable force with (2t-1)² adds algebraic complexity beyond standard constant-force problems, and the multi-step reasoning across 13 marks elevates this above average difficulty. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.03d Newton's second law: 2D vectors |
In this question the unit vectors $\mathbf{i}$ and $\mathbf{j}$ are in the directions east and north respectively.
At time $t$ seconds, where $t \geqslant 0$, a particle $P$ of mass 2 kg is moving on a smooth horizontal surface under the action of a constant horizontal force $(-8\mathbf{i} - 54\mathbf{j})$ N and a variable horizontal force $(4t\mathbf{i} + 6(2t - 1)^2\mathbf{j})$ N.
\begin{enumerate}[label=(\alph*)]
\item Determine the value of $t$ when the forces acting on $P$ are in equilibrium. [2]
\end{enumerate}
It is given that $P$ is at rest when $t = 0$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the speed of $P$ at the instant when $P$ is moving due north. [6]
\item Determine the distance between the positions of $P$ when $t = 0$ and $t = 3$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2021 Q13 [13]}}