| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics B AS (Further Mechanics B AS) |
| Session | Specimen |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Position vector from velocity integration |
| Difficulty | Standard +0.3 This is a straightforward vector mechanics question requiring standard techniques: setting velocity components to zero simultaneously, differentiating velocity to find acceleration then applying F=ma, and integrating velocity with initial conditions. While it involves vectors and multiple steps, each part uses routine A-level further maths methods without requiring problem-solving insight or novel approaches. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation1.10c Magnitude and direction: of vectors3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time3.03b Newton's first law: equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (i) | All 3 components zero at same time |
| Answer | Marks |
|---|---|
| This gives i cpt 0 and k cpt 0. So t = 1 is the only time. | M1 |
| Answer | Marks |
|---|---|
| [3] | 1.1a |
| Answer | Marks |
|---|---|
| 2.1 | This may be implied |
| Answer | Marks | Guidance |
|---|---|---|
| Complete argument | SC1 for t = 1 www. | |
| 1 | (ii) | dv |
| Answer | Marks |
|---|---|
| (cid:169) (cid:185) | M1 |
| Answer | Marks |
|---|---|
| [3] | 1.2 |
| Answer | Marks |
|---|---|
| 1.1 | N |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (iii) | E |
| Answer | Marks |
|---|---|
| (cid:169) (cid:185) | C |
| Answer | Marks |
|---|---|
| [4] | 1.1a |
| Answer | Marks |
|---|---|
| 1.1 | Attempt at integration |
Question 1:
1 | (i) | All 3 components zero at same time
The only possible time is t = 1 (from j cpt)
This gives i cpt 0 and k cpt 0. So t = 1 is the only time. | M1
A1
E1
[3] | 1.1a
1.1
2.1 | This may be implied
This may be obtained by factorising i and j
cpts
Complete argument | SC1 for t = 1 www.
1 | (ii) | dv
a(cid:32)
dt
(cid:167)12t(cid:16)18(cid:183) (cid:167) 6 (cid:183)
(cid:168) (cid:184) (cid:168) (cid:184)
a(cid:32) (cid:16)2 so a(2)(cid:32) (cid:16)2
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:168) (cid:184) (cid:168) (cid:184)
6t 12
(cid:169) (cid:185) (cid:169) (cid:185)
(cid:167) 6 (cid:183)
(cid:168) (cid:184)
Using F = ma F(cid:32)5 (cid:16)2
(cid:168) (cid:184)
(cid:168) (cid:184)
12
(cid:169) (cid:185) | M1
A1
M1
A1
[3] | 1.2
1.1a
1.1
I
1.1 | N
Differentiate w.r.t. t to find a
E
cao
M
Use of F = ma
All correct
Accept any format. cao
1 | (iii) | E
(cid:167)2t3 (cid:16)9t2 (cid:14)12t(cid:14)C(cid:183)
(cid:168) (cid:184)
r(t)(cid:32) 2t(cid:16)t2 (cid:14)D
(cid:168) (cid:184)
(cid:168) t3 (cid:16)3t(cid:14)E (cid:184) P
(cid:169) (cid:185)
(cid:167)(cid:16)5(cid:183)
(cid:168) (cid:184)
Use r(0)(cid:32) 2 S
(cid:168) (cid:184)
(cid:168) (cid:184)
6
(cid:169) (cid:185)
(cid:167)2t3 (cid:16)9t2 (cid:14)12t(cid:16)5(cid:183)
(cid:168) (cid:184)
C = – 5, D = 2, E = 6 r(t)(cid:32) 2t(cid:16)t2 (cid:14)2
(cid:168) (cid:184)
(cid:168) t3 (cid:16)3t(cid:14)6 (cid:184)
(cid:169) (cid:185) | C
M1
A1
M1
A1
A1
[4] | 1.1a
1.1
1.1
1.1
1.1 | Attempt at integration
(cid:100) 2 errors. Accept no arb constants
At least one equation attempted
2 correct
All correct. Full expression given.1 A particle, P , has velocity $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at time $t$ seconds given by $\mathbf { v } = \left( \begin{array} { c } 6 \left( t ^ { 2 } - 3 t + 2 \right) \\ 2 ( 1 - t ) \\ 3 \left( t ^ { 2 } - 1 \right) \end{array} \right)$, where $0 \leq t \leq 3$.\\
(i) Show that there is just one time at which P is instantaneously at rest and state this value of $t$.
P has a mass of 5 kg and is acted on by a single force $\mathbf { F }$ N.\\
(ii) Find $\mathbf { F }$ when $t = 2$.\\
(iii) Find an expression for the position, $\mathbf { r } \mathrm { m }$, of P at time $t \mathrm {~s}$, given that $\mathbf { r } = \left( \begin{array} { c } - 5 \\ 2 \\ 6 \end{array} \right)$ when $t = 0$.
\hfill \mbox{\textit{OCR MEI Further Mechanics B AS Q1 [12]}}