| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics B AS (Further Mechanics B AS) |
| Year | 2019 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | Cartesian equation of path |
| Difficulty | Moderate -0.8 This is a straightforward mechanics question requiring basic differentiation to find force from velocity (F=ma), integration of velocity to find position with initial conditions, and elimination of parameter t to find the Cartesian path equation. All steps are routine applications of standard techniques with no problem-solving insight required. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02e Two-dimensional constant acceleration: with vectors |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | M1 | 1.2 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | A1 | 1.1 |
| Answer | Marks |
|---|---|
| (b) | 2π‘+π |
| Answer | Marks |
|---|---|
| 2 | M1 |
| A1 | 3.4 |
| 1.1 | Condone constants omitted for |
| Answer | Marks |
|---|---|
| attempted | 2π‘ |
| Answer | Marks | Guidance |
|---|---|---|
| Attempt to find constants | M1 | 1.1 |
| Answer | Marks |
|---|---|
| 2 2 | A1 |
| A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| Attempt to eliminate t | M1 | 1.2 |
| Answer | Marks | Guidance |
|---|---|---|
| 8 2 | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | Particle passes through the origin | B1ft |
| origin if their c β 0 | B0 for βstarts at originβ |
Question 3:
3 | (a) | 0
[π =]( )
3 | M1 | 1.2
0
π( )
3 | A1 | 1.1 | Accept 3mj oe | SC If M0 then B1 for 3m
(i.e. not as a vector)
[2]
(b) | 2π‘+π
π₯
( ) = (3 )
π¦ π‘2 β2π‘ +π
2 | M1
A1 | 3.4
1.1 | Condone constants omitted for
M1A1; allow M1 for integration
attempted | 2π‘
π₯
( ) = (3 )+π
π¦ π‘2 β2π‘
2
Attempt to find constants | M1 | 1.1 | Constants might appear as
a separate vector.
2π‘+2
π₯
( ) = (3 1)
π¦ π‘2 β2π‘ β3
2 2 | A1
A1 | 1.1
1.1
Attempt to eliminate t | M1 | 1.2 | Use t ο½ 1 xο1 or their equivalent
2
3 5
π¦ = π₯2 β π₯ [+0]
8 2 | A1 | 1.1
[7]
(c) | Particle passes through the origin | B1ft | 2.2a | Allow does not pass through
origin if their c β 0 | B0 for βstarts at originβ
[1]3 A particle Q of mass $m$ moves in a horizontal plane under the action of a single force $\mathbf { F }$. At time $t , \mathrm { Q }$ has velocity $\binom { 2 } { 3 t - 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Find an expression for $\mathbf { F }$ in terms of $m$.
At time $t$, the displacement of Q is given by $\mathbf { r } = \binom { x } { y }$. When $t = 1 , \mathrm { Q }$ is at the point with position vector $\binom { 4 } { - 4 }$.
\item Find the equation of the path of Q , giving your answer in the form $y = a x ^ { 2 } + b x + c$, where $a$, $b$ and $c$ are constants to be determined.
\item What can you deduce about the path of Q from the value of the constant $c$ you found in part (b)?
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics B AS 2019 Q3 [10]}}