| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2018 |
| Session | December |
| Marks | 6 |
| Topic | Vectors Introduction & 2D |
| Type | Velocity from acceleration and initial conditions |
| Difficulty | Moderate -0.8 This is a straightforward application of constant acceleration (SUVAT) equations in vector form. Part (a) requires finding initial velocity from v = u + at, then using s = ut + ½at². Part (b) uses the initial velocity from (a) to find speed as a magnitude. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial due to vector manipulation and multiple steps. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02e Two-dimensional constant acceleration: with vectors |
| Answer | Marks | Guidance |
|---|---|---|
| \(s = 4(2i + 4j) - \frac{1}{2}(4)^2(3i - 5j)\) | M1 | Attempt use of \(s = vt - \frac{1}{2}at^2\) |
| \(s = (-16i + 56j)m\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(2i + 4j = u + 4(3i - 5j)\) | M1* | Attempt use of \(v = u + at\) |
| \(\mathbf{u} = -10i + 24j\) | A1 | |
| \( | \mathbf{u} | = \sqrt{(-10)^2 + 24^2} = 26 \text{ ms}^{-1}\) |
| \(= 26 \text{ ms}^{-1}\) | A1 |
## Part (a)
$s = 4(2i + 4j) - \frac{1}{2}(4)^2(3i - 5j)$ | M1 | Attempt use of $s = vt - \frac{1}{2}at^2$ | Accept equivalent full methods using suvat equations e.g. first using $v = u + at$ to find $u$ and then using $s = ut + \frac{1}{2}at^2$
$s = (-16i + 56j)m$ | A1 |
## Part (b)
$2i + 4j = u + 4(3i - 5j)$ | M1* | Attempt use of $v = u + at$
$\mathbf{u} = -10i + 24j$ | A1 |
$|\mathbf{u}| = \sqrt{(-10)^2 + 24^2} = 26 \text{ ms}^{-1}$ | M1dep* | Attempt magnitude of their $\mathbf{u}$
$= 26 \text{ ms}^{-1}$ | A1 |A particle $P$ moves with constant acceleration $(3\mathbf{i} - 5\mathbf{j})\text{m s}^{-2}$. At time $t = 0$ seconds $P$ is at the origin. At time $t = 4$ seconds $P$ has velocity $(2\mathbf{i} + 4\mathbf{j})\text{m s}^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Find the displacement vector of $P$ at time $t = 4$ seconds. [2]
\item Find the speed of $P$ at time $t = 0$ seconds. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2018 Q7 [6]}}