| Exam Board | WJEC |
|---|---|
| Module | Unit 4 (Unit 4) |
| Year | 2019 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Vector motion with components |
| Difficulty | Standard +0.3 This is a straightforward mechanics question requiring standard differentiation and integration of trigonometric functions. Part (a) uses F=ma with differentiation, part (b) requires integration with initial conditions, and part (c) is simple substitution and magnitude calculation. All techniques are routine A-level mechanics with no problem-solving insight needed, making it slightly easier than average. |
| Spec | 1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)3.02g Two-dimensional variable acceleration3.03d Newton's second law: 2D vectors |
A particle $P$ of mass $0.5$ kg moves on a horizontal plane such that its velocity vector $\mathbf{v}$ ms$^{-1}$ at time $t$ seconds is given by
$$\mathbf{v} = 12\cos(3t)\mathbf{i} - 5\sin(2t)\mathbf{j}.$$
\begin{enumerate}[label=(\alph*)]
\item Find an expression for the force acting on $P$ at time $t$ s. [3]
\item Given that when $t = 0$, $P$ has position vector $(\mathbf{4i} + \mathbf{7j})$ m relative to the origin $O$, find an expression for the position vector of $P$ at time $t$ s. [4]
\item Hence determine the distance of $P$ from $O$ at time $t = \frac{\pi}{2}$. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 4 2019 Q6 [9]}}