| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 9 |
| Topic | Variable acceleration (1D) |
| Type | Vector motion with components |
| Difficulty | Standard +0.3 This is a standard M1 kinematics question requiring differentiation of position vectors to find velocity and acceleration, then applying F=ma. Part (a) involves finding velocity direction (routine), part (b) applies Newton's second law (standard), and part (c) solves a simple equation for when velocity components are equal. All techniques are textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02g Two-dimensional variable acceleration3.03d 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.
A particle of mass 0.12 kg is moving so that its position vector $\mathbf{r}$ metres at time $t$ seconds is given by
$\mathbf{r} = 2t^2\mathbf{i} + (5t^2 - 4t)\mathbf{j}$.
\begin{enumerate}[label=(\alph*)]
\item Show that when $t = 0.7$ the bearing on which the particle is moving is approximately $044°$. [3]
\item Find the magnitude of the resultant force acting on the particle at the instant when $t = 0.7$. [4]
\item Determine the times at which the particle is moving on a bearing of $045°$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2017 Q11 [9]}}