| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Displacement from velocity by integration |
| Difficulty | Moderate -0.8 This is a straightforward mechanics question requiring basic calculus operations: integrating velocity to find displacement (with initial condition) and differentiating velocity to find acceleration. Both are standard A-level techniques with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature and need to apply the initial condition correctly. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02f Non-uniform acceleration: using differentiation and integration |
A particle $P$, of mass 3 kg, moves along the horizontal $x$-axis under the action of a resultant force $F$ N. Its velocity $v$ ms$^{-1}$ at time $t$ seconds is given by
$$v = 12t - 3t^2.$$
\begin{enumerate}[label=(\alph*)]
\item Given that the particle is at the origin $O$ when $t = 1$, find an expression for the displacement of the particle from $O$ at time $t$ s. [3]
\item Find an expression for the acceleration of the particle at time $t$ s. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 Q8 [5]}}