| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Velocity from acceleration and initial conditions |
| Difficulty | Moderate -0.3 This is a straightforward M1 kinematics question requiring standard techniques: finding when y=0 (basic algebra), differentiating position to get velocity (routine calculus), and eliminating the parameter t (standard method). All parts are textbook exercises with no problem-solving insight required, making it slightly easier than average, though the multi-part structure and parameter elimination prevent it from being trivial. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time |
Fig. 4 shows the unit vectors $\mathbf{i}$ and $\mathbf{j}$ in the directions of the cartesian axes $Ox$ and $Oy$, respectively. O is the origin of the axes and of position vectors.
\includegraphics{figure_1}
The position vector of a particle is given by $\mathbf{r} = 3t\mathbf{i} + (18t^2 - 11)\mathbf{j}$ for $t \geq 0$, where $t$ is time.
\begin{enumerate}[label=(\roman*)]
\item Show that the path of the particle cuts the $x$-axis just once. [2]
\item Find an expression for the velocity of the particle at time $t$.
Deduce that the particle never travels in the $\mathbf{j}$ direction. [3]
\item Find the cartesian equation of the path of the particle, simplifying your answer. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M1 Q2 [8]}}