| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2012 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Vector motion with components |
| Difficulty | Standard +0.3 This is a straightforward mechanics question requiring application of F=ma to find acceleration, then integration with initial conditions to find velocity, and finally calculating speed from velocity components. While it involves vectors and exponential functions, each step follows standard procedures with no novel problem-solving required. The integration of e^(-2t) and polynomial terms is routine for M2 level, making this slightly easier than average. |
| Spec | 1.06b Gradient of e^(kx): derivative and exponential model1.08h Integration by substitution1.10b Vectors in 3D: i,j,k notation3.02a Kinematics language: position, displacement, velocity, acceleration3.02f Non-uniform acceleration: using differentiation and integration3.03d Newton's second law: 2D vectors |
2 A particle, of mass 50 kg , moves on a smooth horizontal plane. A single horizontal force
$$\left[ \left( 300 t - 60 t ^ { 2 } \right) \mathbf { i } + 100 \mathrm { e } ^ { - 2 t } \mathbf { j } \right] \text { newtons }$$
acts on the particle at time $t$ seconds.\\
The vectors $\mathbf { i }$ and $\mathbf { j }$ are perpendicular unit vectors.
\begin{enumerate}[label=(\alph*)]
\item Find the acceleration of the particle at time $t$.
\item When $t = 0$, the velocity of the particle is $( 7 \mathbf { i } - 4 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$.
Find the velocity of the particle at time $t$.
\item Calculate the speed of the particle when $t = 1$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2012 Q2 [10]}}