| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Position from velocity and initial conditions |
| Difficulty | Moderate -0.8 This is a straightforward M1 kinematics question requiring basic vector operations: (a) uses tan^(-1)(2/3) to find angle, and (b) applies r = r₀ + vt then calculates magnitude. Both parts are standard textbook exercises with clear methods and minimal problem-solving demand, making it easier than average but not trivial due to the vector manipulation required. |
| Spec | 1.10c Magnitude and direction: of vectors1.10f Distance between points: using position vectors |
| Answer | Marks |
|---|---|
| req'd angle \(= \tan^{-1} \frac{4}{3} = 33.7°\) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| when \(t = 2\), posn. vector of \(A\) is \((2 + 6j) + (11 + 4j)j = 8i + 15j\) | M1 A1 | |
| \(OP = \sqrt{8^2 + 15^2} = 17\) m | M1 A1 | (6) |
**Part (a):**
req'd angle $= \tan^{-1} \frac{4}{3} = 33.7°$ | M1 A1 |
**Part (b):**
when $t = 2$, posn. vector of $A$ is $(2 + 6j) + (11 + 4j)j = 8i + 15j$ | M1 A1 |
$OP = \sqrt{8^2 + 15^2} = 17$ m | M1 A1 | (6)
---A particle $P$ moves with a constant velocity $(3\mathbf{i} + 2\mathbf{j})$ m s$^{-1}$ with respect to a fixed origin $O$. It passes through the point $A$ whose position vector is $(2\mathbf{i} + 11\mathbf{j})$ m at $t = 0$.
\begin{enumerate}[label=(\alph*)]
\item Find the angle in degrees that the velocity vector of $P$ makes with the vector $\mathbf{i}$. [2 marks]
\item Calculate the distance of $P$ from $O$ when $t = 2$. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [6]}}