| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find final speed |
| Difficulty | Moderate -0.8 This is a straightforward application of conservation of momentum in one dimension with clearly defined scenarios. Part (a) requires a single-step calculation with one unknown, and part (b) involves setting up one equation with one unknown. Both parts are routine M1 collision problems requiring only direct substitution into the momentum conservation formula, making this easier than average. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(2 \times 6 = 3 \times v\) | M1 | |
| \(v = 4 \text{ ms}^{-1}\) | A1, A1 | Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(2 \times 6 = -2 \times v + 3 \times 4v\) | M1, A1 | all terms |
| \(12 = 10v\) | ||
| \(v = 1.2 \text{ ms}^{-1}\) | A1\(\sqrt{}\) | Total: 3 |
## Question 1:
### Part (a)
| Working | Marks | Guidance |
|---------|-------|----------|
| $2 \times 6 = 3 \times v$ | M1 | |
| $v = 4 \text{ ms}^{-1}$ | A1, A1 | Total: 3 |
### Part (b)
| Working | Marks | Guidance |
|---------|-------|----------|
| $2 \times 6 = -2 \times v + 3 \times 4v$ | M1, A1 | all terms |
| $12 = 10v$ | | |
| $v = 1.2 \text{ ms}^{-1}$ | A1$\sqrt{}$ | Total: 3 | $\sqrt{}$ sign error ($v = 0.857$) |
---1 A particle $A$ moves across a smooth horizontal surface in a straight line. The particle $A$ has mass 2 kg and speed $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. A particle $B$, which has mass 3 kg , is at rest on the surface. The particle $A$ collides with the particle $B$.\\
\includegraphics[max width=\textwidth, alt={}, center]{c220e6c4-2676-4022-8301-7d720dc082b2-2_147_506_644_733}
\begin{enumerate}[label=(\alph*)]
\item If, after the collision, $A$ is at rest and $B$ moves away from $A$, find the speed of $B$.
\item If, after the collision, $A$ and $B$ move away from each other with speeds $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $4 v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively, as shown in the diagram below, find the value of $v$.\\
\includegraphics[max width=\textwidth, alt={}, center]{c220e6c4-2676-4022-8301-7d720dc082b2-2_138_506_1144_730}
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2006 Q1 [6]}}