| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2006 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Vector impulse: find velocity or speed after impulse |
| Difficulty | Moderate -0.3 This is a straightforward M2 question requiring standard differentiation of position vectors to find velocity, calculating speed as magnitude, then applying the impulse-momentum equation. All steps are routine with no problem-solving insight needed, making it slightly easier than average but not trivial due to the algebraic manipulation and multi-step nature. |
| Spec | 1.10c Magnitude and direction: of vectors3.02a Kinematics language: position, displacement, velocity, acceleration6.03f Impulse-momentum: relation |
A particle $P$ of mass 0.4 kg is moving so that its position vector $\mathbf{r}$ metres at time $t$ seconds is given by
$$\mathbf{r} = (t^2 + 4t)\mathbf{i} + (3t - t^3)\mathbf{j}.$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the speed of $P$ when $t = 3$. [5]
\end{enumerate}
When $t = 3$, the particle $P$ is given an impulse $(8\mathbf{i} - 12\mathbf{j})$ N s.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the velocity of $P$ immediately after the impulse. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2006 Q2 [8]}}