| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Major (Further Mechanics Major) |
| Year | 2020 |
| Session | November |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | Particle moving perpendicular to vector |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths mechanics question requiring differentiation of position vectors, dot product for perpendicularity, and distance calculation. All steps are routine applications of standard techniques with no conceptual challenges—slightly easier than average due to its mechanical nature, though the multi-part structure and Further Maths context keep it near the mean. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | v=20i+(10−10t) |
| j | M1* | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| Setting t = 0 | M1dep* | 1.1 |
| v=20i+10j | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | 20 20 |
| Answer | Marks | Guidance |
|---|---|---|
| 10 10−10T | M1* | 3.4 |
| Answer | Marks | Guidance |
|---|---|---|
| 400+10(10−10T)=0 | M1dep* | 1.1 |
| linear equation in T | Allow in terms of t | |
| T =5 | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (c) | t=0,r=5i+95j |
| t =5,r=105i+20j | B1ft | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (105i+20j )−(5i+95j )=100i−75j | M1 | 1.1 |
| Distance is 125 | A1 | 1.1 |
Question 4:
4 | (a) | v=20i+(10−10t)
j | M1* | 1.1 | Attempt at differentiation – at least one
component correct
Setting t = 0 | M1dep* | 1.1 | Substituting t = 0 into their v
v=20i+10j | A1 | 1.1
[3]
4 | (b) | 20 20
⋅ =0
10 10−10T | M1* | 3.4 | Setting up scalar product with their initial
v and v and equating to zero
400+10(10−10T)=0 | M1dep* | 1.1 | Correct use of scalar product to form a
linear equation in T | Allow in terms of t
T =5 | A1 | 1.1
[3]
4 | (c) | t=0,r=5i+95j | B1 | 1.1
t =5,r=105i+20j | B1ft | 1.1 | Follow through their value of T
Displacement vector
(105i+20j )−(5i+95j )=100i−75j | M1 | 1.1 | Difference in their r values
Distance is 125 | A1 | 1.1
[4]A particle P moves so that its position vector $\mathbf{r}$ at time $t$ is given by
$$\mathbf{r} = (5 + 20t)\mathbf{i} + (95 + 10t - 5t^2)\mathbf{j}.$$
\begin{enumerate}[label=(\alph*)]
\item Determine the initial velocity of P. [3]
At time $t = T$, P is moving in a direction perpendicular to its initial direction of motion.
\item Determine the value of $T$. [3]
\item Determine the distance of P from its initial position at time $T$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2020 Q4 [10]}}