| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2019 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | Find unknown constant from motion condition |
| Difficulty | Standard +0.3 This is a standard A-level mechanics question involving differentiation of velocity to find force, integration to find position, and using geometric constraints. Part (a) requires F=ma with differentiation and magnitude calculation (routine but multi-step). Parts (b) and (c) involve straightforward integration and solving a linear equation using the line condition. All techniques are standard with no novel insight required, making it slightly easier than average. |
| Spec | 3.03n Equilibrium in 2D: particle under forces3.04b Equilibrium: zero resultant moment and force |
In this question the unit vectors $\mathbf{i}$ and $\mathbf{j}$ are in the directions east and north respectively.
A particle $R$ of mass $2$ kg is moving on a smooth horizontal surface under the action of a single horizontal force $\mathbf{F}$ N. At time $t$ seconds, the velocity $\mathbf{v} \text{ m s}^{-1}$ of $R$, relative to a fixed origin $O$, is given by $\mathbf{v} = (pt^2 - 3t)\mathbf{i} + (8t + q)\mathbf{j}$, where $p$ and $q$ are constants and $p < 0$.
\begin{enumerate}[label=(\alph*)]
\item Given that when $t = 0.5$ the magnitude of $\mathbf{F}$ is $20$, find the value of $p$. [6]
\end{enumerate}
When $t = 0$, $R$ is at the point with position vector $(2\mathbf{i} - 3\mathbf{j})$ m.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{1}
\item Find, in terms of $q$, an expression for the displacement vector of $R$ at time $t$. [4]
\end{enumerate}
When $t = 1$, $R$ is at a point on the line $L$, where $L$ passes through $O$ and the point with position vector $2\mathbf{i} - 8\mathbf{j}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{2}
\item Find the value of $q$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2019 Q10 [13]}}