| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2006 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Displacement from velocity by integration |
| Difficulty | Moderate -0.3 This is a straightforward calculus mechanics question requiring differentiation of v to find acceleration, integration of v to find displacement, and basic analysis of an exponential function. All steps are routine applications of standard techniques with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.07a Derivative as gradient: of tangent to curve1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx) |
3 A particle moves in a straight line and at time $t$ has velocity $v$, where
$$v = 2 t - 12 \mathrm { e } ^ { - t } , \quad t \geqslant 0$$
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find an expression for the acceleration of the particle at time $t$.
\item State the range of values of the acceleration of the particle.
\end{enumerate}\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 2006 Q3 [9]}}