| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2012 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Displacement from velocity by integration |
| Difficulty | Moderate -0.3 This is a straightforward mechanics question requiring standard differentiation of a polynomial-exponential function, substitution, applying F=ma, and integration with initial conditions. All techniques are routine M2 content with no problem-solving insight needed, making it slightly easier than average but not trivial due to the exponential term and multiple parts. |
| Spec | 1.08d Evaluate definite integrals: between limits3.02f Non-uniform acceleration: using differentiation and integration3.03d Newton's second law: 2D vectors |
2 A particle moves in a straight line. At time $t$ seconds, it has velocity $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, where
$$v = 6 t ^ { 2 } - 2 \mathrm { e } ^ { - 4 t } + 8$$
and $t \geqslant 0$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find an expression for the acceleration of the particle at time $t$.
\item Find the acceleration of the particle when $t = 0.5$.
\end{enumerate}\item The particle has mass 4 kg .
Find the magnitude of the force acting on the particle when $t = 0.5$.
\item When $t = 0$, the particle is at the origin.
Find an expression for the displacement of the particle from the origin at time $t$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2012 Q2 [9]}}