| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Force from vector acceleration |
| Difficulty | Moderate -0.5 This is a straightforward mechanics question requiring routine differentiation of displacement to find velocity, then acceleration, followed by applying F=ma. The 'show that' part involves simple verification that the second derivative is constant (no t terms), and finding magnitude is basic vector arithmetic. Below average difficulty as it's purely procedural with no problem-solving or insight required. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.03d Newton's second law: 2D vectors |
| Answer | Marks |
|---|---|
| \(v = \frac{dr}{dt} = 6t - 8j\) | M1 A1 |
| \(a = \frac{dv}{dt} = 6i - 8j\) not dependent on \(t\) so constant | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(F = ma = 2a = | 2i - 16j | \) |
| \(\text{mag. of } F = \sqrt{(12)^2 + (16)^2} = 20 \text{ N}\) | M1 A1 | (7) |
**Part (a):**
$v = \frac{dr}{dt} = 6t - 8j$ | M1 A1 |
$a = \frac{dv}{dt} = 6i - 8j$ not dependent on $t$ so constant | M1 A1 |
**Part (b):**
$F = ma = 2a = |2i - 16j|$ | A1 |
$\text{mag. of } F = \sqrt{(12)^2 + (16)^2} = 20 \text{ N}$ | M1 A1 | (7)
---\begin{enumerate}
\item A particle $P$ of mass 2 kg is subjected to a force $\mathbf { F }$ such that its displacement, $\mathbf { r }$ metres, from a fixed origin, $O$, at time $t$ seconds is given by
\end{enumerate}
$$\mathbf { r } = \left( 3 t ^ { 2 } - 4 \right) \mathbf { i } + \left( 3 - 4 t ^ { 2 } \right) \mathbf { j }$$
(a) Show that the acceleration of $P$ is constant.\\
(b) Find the magnitude of $\mathbf { F }$.\\
\hfill \mbox{\textit{Edexcel M2 Q1 [7]}}