| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Forces in vector form: resultant and acceleration |
| Difficulty | Moderate -0.8 This is a straightforward M1 kinematics question requiring only direct application of standard formulae (v = u + at and F = ma) with vector notation. All three parts involve routine calculations with no problem-solving insight needed, making it easier than average for A-level. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.03c Newton's second law: F=ma one dimension |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \((i + 2j)\) ms\(^{-1}\) | M1 A1; M1 A1 | |
| (b) \(\sqrt{(7^2 + 14^2)} = 7\sqrt{5}\) or \(15.7\) ms\(^{-1}\) | A1; M1 A1 | |
| on bearing \(\tan^{-1} 0.5 = 026.6°\) | ||
| (c) \(2.5\sqrt{5} = 5.59\) N | A1; M1 A1 | Total: 7 marks |
**(a)** $(i + 2j)$ ms$^{-1}$ | M1 A1; M1 A1 |
**(b)** $\sqrt{(7^2 + 14^2)} = 7\sqrt{5}$ or $15.7$ ms$^{-1}$ | A1; M1 A1 |
on bearing $\tan^{-1} 0.5 = 026.6°$ | |
**(c)** $2.5\sqrt{5} = 5.59$ N | A1; M1 A1 | **Total: 7 marks**A particle $P$, of mass $2.5$ kg, initially at rest at the point $O$, moves on a smooth horizontal surface with constant acceleration $(\mathbf{i} + 2\mathbf{j})$ ms$^{-2}$, where $\mathbf{i}$ and $\mathbf{j}$ are unit vectors in the directions due East and due North respectively. Find
\begin{enumerate}[label=(\alph*)]
\item the velocity vector of $P$ at time $t$ seconds after it leaves $O$, \hfill [2 marks]
\item the magnitude and direction of the velocity of $P$ when $t = 7$, \hfill [3 marks]
\item the magnitude, in N, of the force acting on $P$. \hfill [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q1 [7]}}