| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Position vector from velocity integration |
| Difficulty | Standard +0.3 This is a straightforward integration problem requiring students to integrate polynomial and exponential functions component-wise, then apply initial conditions to find constants. While it involves vectors and exponential functions, the techniques are standard M2 material with no conceptual challenges—slightly easier than average due to its routine nature. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02e Two-dimensional constant acceleration: with vectors3.02f Non-uniform acceleration: using differentiation and integration |
3 A particle, of mass 10 kg , moves on a smooth horizontal plane. At time $t$ seconds, the acceleration of the particle is given by
$$\left\{ \left( 40 t + 3 t ^ { 2 } \right) \mathbf { i } + 20 \mathrm { e } ^ { - 4 t } \mathbf { j } \right\} \mathrm { m } \mathrm {~s} ^ { - 2 }$$
where the vectors $\mathbf { i }$ and $\mathbf { j }$ are perpendicular unit vectors.
\begin{enumerate}[label=(\alph*)]
\item At time $t = 1$, the velocity of the particle is $\left( 6 \mathbf { i } - 5 \mathrm { e } ^ { - 4 } \mathbf { j } \right) \mathrm { m } \mathrm { s } ^ { - 1 }$.
Find the velocity of the particle at time $t$.
\item Calculate the initial speed of the particle.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2013 Q3 [8]}}