| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Work done by constant force - vector setup |
| Difficulty | Standard +0.3 This is a straightforward M2 work-energy question requiring standard vector displacement calculation (PQ = Q - P), work done formula (F·d), and work-energy principle (work = ΔKE). All steps are routine applications of well-practiced formulas with no conceptual challenges or novel problem-solving required, making it slightly easier than average. |
| Spec | 1.10d Vector operations: addition and scalar multiplication1.10g Problem solving with vectors: in geometry6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component6.02e Calculate KE and PE: using formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Displacement \(= 12\mathbf{i} + 15\mathbf{j}\) | M1 A1 A1 | |
| Distance \(= 3\sqrt{41}\) | M1 | |
| \( | \mathbf{F} | = \sqrt{41}\), so work done \(= 3\sqrt{41} \times \sqrt{41} = 123\) J |
| (b) \(a = 4\mathbf{i} + 5\mathbf{j}\) | B1 M1 A1 | |
| \(12\mathbf{i} + 15\mathbf{j} = \frac{1}{2}(4\mathbf{i} + 5\mathbf{j})t^2\) | M1 | |
| \(t = \sqrt{6}\) | A1 | |
| \(\mathbf{v} = \sqrt{6}(4\mathbf{i} + 5\mathbf{j})\) | M1 | |
| \( | \mathbf{v} | = \sqrt{246} = 15 \cdot 7\) ms\(^{-1}\) |
(a) Displacement $= 12\mathbf{i} + 15\mathbf{j}$ | M1 A1 A1 |
Distance $= 3\sqrt{41}$ | M1 |
$|\mathbf{F}| = \sqrt{41}$, so work done $= 3\sqrt{41} \times \sqrt{41} = 123$ J | A1 |
(b) $a = 4\mathbf{i} + 5\mathbf{j}$ | B1 M1 A1 |
$12\mathbf{i} + 15\mathbf{j} = \frac{1}{2}(4\mathbf{i} + 5\mathbf{j})t^2$ | M1 |
$t = \sqrt{6}$ | A1 |
$\mathbf{v} = \sqrt{6}(4\mathbf{i} + 5\mathbf{j})$ | M1 |
$|\mathbf{v}| = \sqrt{246} = 15 \cdot 7$ ms$^{-1}$ | A1 | (10 marks)$\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors in a horizontal plane. A body of mass 1 kg moves under the action of a constant force $(4\mathbf{i} + 5\mathbf{j})$ N. The body moves from the point $P$ with position vector $(-3\mathbf{i} - 15\mathbf{j})$ m to the point $Q$ with position vector $9\mathbf{i}$ m.
\begin{enumerate}[label=(\alph*)]
\item Find the work done by the force in moving the body from $P$ to $Q$. [5 marks]
\item Given that the body started from rest at $P$, find its speed when it is at $Q$. [5 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q4 [10]}}