| Exam Board | OCR |
|---|---|
| Module | Further Mechanics (Further Mechanics) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Impulse from variable force (then find velocity) |
| Difficulty | Standard +0.3 This is a straightforward application of impulse-momentum theorem with integration. Students must integrate a polynomial-exponential function (standard A-level technique) and apply I = mv - mu. The integration is routine for Further Maths students, and the two-part structure guides them through the solution methodically. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (i) | p |
| Answer | Marks |
|---|---|
| 0 3 | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| 1.1 | Integrating one term of F correctly | |
| BC | 182.1277… | |
| 3 | (ii) | 2(v(cid:16)5)(cid:32)55(cid:14)3e4 |
| Answer | Marks |
|---|---|
| Speed is 96.1ms-1 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 3.4 | |
| 1.1 | Use of I (cid:32)mv(cid:16)mu | 96.0638… |
Question 3:
3 | (i) | p
S
I (cid:32)(cid:179)t2(cid:14)3etdt(cid:32)1t3(cid:14)3et
3
4
I (cid:32)(cid:179) Fdt(cid:32)55(cid:14)3e4 (cid:32)182, so impulse is 182Ns
0 3 | M1
A1
A1
[3] | 3.3
1.1
1.1 | Integrating one term of F correctly
BC | 182.1277…
3 | (ii) | 2(v(cid:16)5)(cid:32)55(cid:14)3e4
3
Speed is 96.1ms-1 | M1
A1
[2] | 3.4
1.1 | Use of I (cid:32)mv(cid:16)mu | 96.0638…3 A body, $Q$, of mass 2 kg moves in a straight line under the action of a single force which acts in the direction of motion of $Q$. Initially the speed of $Q$ is $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. At time $t \mathrm {~s}$, the magnitude $F \mathrm {~N}$ of the force is given by
$$F = t ^ { 2 } + 3 \mathrm { e } ^ { t } , \quad 0 \leq t \leq 4$$
(i) Calculate the impulse of the force over the time interval.\\
(ii) Hence find the speed of $Q$ when $t = 4$.
\hfill \mbox{\textit{OCR Further Mechanics Q3 [5]}}