| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2002 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Force from vector acceleration |
| Difficulty | Standard +0.3 This is a straightforward M2 question requiring standard application of F=ma (differentiating velocity to find acceleration, then multiplying by mass) and integration of velocity to find position. Both parts follow routine procedures with no problem-solving insight needed, making it slightly easier than average but not trivial due to vector components and multi-step calculations. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time3.03d Newton's second law: 2D vectors |
A particle $P$ of mass 0.3 kg is moving under the action of a single force $\mathbf{F}$ newtons. At time $t$ seconds the velocity of $P$, $\mathbf{v}$ m s$^{-1}$, is given by
$$\mathbf{v} = 3t\mathbf{i} + (6t - 4)\mathbf{j}.$$
\begin{enumerate}[label=(\alph*)]
\item Calculate, to 3 significant figures, the magnitude of $\mathbf{F}$ when $t = 2$.
[5]
\end{enumerate}
When $t = 0$, $P$ is at the point $A$. The position vector of $A$ with respect to a fixed origin $O$ is $(3\mathbf{i} - 4\mathbf{j})$ m. When $t = 4$, $P$ is at the point $B$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the position vector of $B$.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2002 Q3 [10]}}