| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Vector motion with components |
| Difficulty | Standard +0.3 This is a straightforward M2 mechanics question requiring application of Newton's second law (F=ma) followed by integration to find velocity, then calculating speed as magnitude. All steps are routine: divide force by mass, integrate component-wise with given initial conditions, and find magnitude. While it involves vector calculus and exponential/polynomial functions, these are standard M2 techniques with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02g Two-dimensional variable acceleration3.03d Newton's second law: 2D vectors |
A particle has mass 6 kg. A single force $(24e^{-2t}\mathbf{i} - 12t^3\mathbf{j})$ newtons acts on the particle at time $t$ seconds. No other forces act on the particle.
\begin{enumerate}[label=(\alph*)]
\item Find the acceleration of the particle at time $t$. [2 marks]
\item At time $t = 0$, the velocity of the particle is $(-7\mathbf{i} - 4\mathbf{j}) \text{ m s}^{-1}$.
Find the velocity of the particle at time $t$. [4 marks]
\item Find the speed of the particle when $t = 0.5$. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2014 Q2 [10]}}