| Exam Board | WJEC |
|---|---|
| Module | Further Unit 3 (Further Unit 3) |
| Year | 2024 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | 3D vector motion problems |
| Difficulty | Standard +0.8 This is a further maths mechanics question requiring integration of a vector force (with non-standard term √t), finding velocity from F=ma, applying initial conditions, then solving a perpendicular vector condition using dot product equals zero. The multi-step nature, further maths context, and non-routine √t term place it moderately above average difficulty. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication3.03d Newton's second law: 2D vectors |
5. A particle of mass 2 kg is moving under the action of a force $\mathbf { F N }$ which, at time $t$ seconds, is given by
$$\mathbf { F } = 4 t \mathbf { i } - \sqrt { t } \mathbf { j } + 6 \mathbf { k }$$
When $t = 1$, the velocity of the particle is $\left( 3 \mathbf { i } - \frac { 1 } { 3 } \mathbf { j } - \mathbf { k } \right) \mathrm { ms } ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Find an expression for the velocity vector of the particle at time $t \mathrm {~s}$.
\item Determine the values of $t$ when the particle is moving in a direction perpendicular to the vector $( - \mathbf { i } + 3 \mathbf { k } )$.
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 3 2024 Q5 [9]}}