| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | SUVAT in 2D & Gravity |
| Type | Particle motion: 2D constant acceleration |
| Difficulty | Moderate -0.3 This is a straightforward 2D kinematics problem requiring standard application of SUVAT equations with vectors. Part (a) tests understanding of Newton's second law (constant force → constant acceleration), while part (b) involves routine vector arithmetic to find acceleration from velocity change, then magnitude and angle calculations. All steps are mechanical with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication1.10h Vectors in kinematics: uniform acceleration in vector form3.03d Newton's second law: 2D vectors3.03f Weight: W=mg |
| Answer | Marks | Guidance |
|---|---|---|
| (a) mass of ball remains constant, force is constant | B2 | |
| \(F = ma\) so a constant | ||
| (b)(i) \(a = \frac{\Delta v}{\Delta t} = \frac{1}{2}[(10\mathbf{i} + 9\mathbf{j}) - (2\mathbf{i} - 3\mathbf{j})] = 2\mathbf{i} + 3\mathbf{j}\) | M1 A1 | |
| mag. of \(a = \sqrt{2^2 + 3^2} = \sqrt{13} = 3.61 \text{ ms}^{-2}\) | M1 A1 | (3sf) |
| (b)(ii) \(F = ma = 2(2\mathbf{i} + 3\mathbf{j}) = 4\mathbf{i} + 6\mathbf{j}\) | M1 | |
| req'd angle \(= \tan^{-1}\frac{3}{2} = 56.3°\) | M1 A1 | (3sf) |
**(a)** mass of ball remains constant, force is constant | B2 |
$F = ma$ so a constant | |
**(b)(i)** $a = \frac{\Delta v}{\Delta t} = \frac{1}{2}[(10\mathbf{i} + 9\mathbf{j}) - (2\mathbf{i} - 3\mathbf{j})] = 2\mathbf{i} + 3\mathbf{j}$ | M1 A1 |
mag. of $a = \sqrt{2^2 + 3^2} = \sqrt{13} = 3.61 \text{ ms}^{-2}$ | M1 A1 | (3sf)
**(b)(ii)** $F = ma = 2(2\mathbf{i} + 3\mathbf{j}) = 4\mathbf{i} + 6\mathbf{j}$ | M1 |
req'd angle $= \tan^{-1}\frac{3}{2} = 56.3°$ | M1 A1 | (3sf) | (9)2. A ball of mass 2 kg moves on a smooth horizontal surface under the action of a constant force, $\mathbf { F }$. The initial velocity of the ball is $( 2 \mathbf { i } - 3 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$ and 4 seconds later it has velocity $( 10 \mathbf { i } + 9 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ where $\mathbf { i }$ and $\mathbf { j }$ are perpendicular, horizontal unit vectors.
\begin{enumerate}[label=(\alph*)]
\item Making reference to the mass of the ball and the force it experiences, explain why it is reasonable to assume that the acceleration is constant.
\item Find, giving your answers correct to 3 significant figures,
\begin{enumerate}[label=(\roman*)]
\item the magnitude of the acceleration experienced by the ball,
\item the angle which $\mathbf { F }$ makes with the vector $\mathbf { i }$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [9]}}