| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2009 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Distance from velocity-time graph |
| Difficulty | Moderate -0.8 This is a straightforward velocity-time graph question requiring only reading values from the graph and calculating areas of simple geometric shapes (triangles/trapezoids). Part (b) is shown for students, and all parts involve standard M1 techniques with no problem-solving insight needed—easier than average A-level. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(t = 0\), \(t = 30\), \(t = 50\) seconds | B1 | Any one correct time |
| B1 | The other two correct times. Deduct one mark for each extra time given. Condone 49 or 48 instead of 50 | |
| Total: 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(s_1 = \frac{1}{2} \times 30 \times 5 = 75 \text{ m}\) AG | M1 | Finding distance by calculation of area. Must see use of 0.5 or \(\frac{1}{2}\) |
| A1 | Correct answer from correct working. If candidates use two constant acceleration equations, both must be seen for M1 mark | |
| Total: 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(s_2 = \frac{1}{2} \times 4 \times 20 = 40 \text{ m}\) | M1 | Finding distance using area of the second triangle |
| A1 | Correct distance (ignore any negative signs). If candidates use two constant acceleration equations, both must be seen for M1 mark. Accept 38/36 from use of 49/48 instead of 50 | |
| \(s = 75 + 40 = 115 \text{ m}\) | M1 | Addition of the 75 metres and their distance. \((75 - 40 = 35\) OE scores M0\()\) |
| A1F | Correct result using their value for second area. Accept 113/111 from use of 49/48 instead of 50 | |
| Total: 4 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(s = 75 - 40 = 35 \text{ m}\) | M1 | Difference between 75 and their value for the second distance. Allow their distance \(- 75\). \((75 - (-40) = 115\) OE scores M0\()\) |
| A1F | Correct result using their value for second area. \((eg\ 40 - 75 = -35\) M1A0\()\). Accept 37/39 from use of 49/48 instead of 50 | |
| Total: 2 marks |
## Question 2:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $t = 0$, $t = 30$, $t = 50$ seconds | B1 | Any one correct time |
| | B1 | The other two correct times. Deduct one mark for each extra time given. Condone 49 or 48 instead of 50 |
| **Total: 2 marks** | | |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $s_1 = \frac{1}{2} \times 30 \times 5 = 75 \text{ m}$ **AG** | M1 | Finding distance by calculation of area. Must see use of 0.5 or $\frac{1}{2}$ |
| | A1 | Correct answer from correct working. If candidates use two constant acceleration equations, both must be seen for M1 mark |
| **Total: 2 marks** | | |
### Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $s_2 = \frac{1}{2} \times 4 \times 20 = 40 \text{ m}$ | M1 | Finding distance using area of the second triangle |
| | A1 | Correct distance (ignore any negative signs). If candidates use two constant acceleration equations, both must be seen for M1 mark. Accept 38/36 from use of 49/48 instead of 50 |
| $s = 75 + 40 = 115 \text{ m}$ | M1 | Addition of the 75 metres and their distance. $(75 - 40 = 35$ OE scores M0$)$ |
| | A1F | Correct result using their value for second area. Accept 113/111 from use of 49/48 instead of 50 |
| **Total: 4 marks** | | |
### Part (d):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $s = 75 - 40 = 35 \text{ m}$ | M1 | Difference between 75 and their value for the second distance. Allow their distance $- 75$. $(75 - (-40) = 115$ OE scores M0$)$ |
| | A1F | Correct result using their value for second area. $(eg\ 40 - 75 = -35$ M1A0$)$. Accept 37/39 from use of 49/48 instead of 50 |
| **Total: 2 marks** | | |
---2 The graph shows how the velocity of a particle varies during a 50 -second period as it moves forwards and then backwards on a straight line.\\
\includegraphics[max width=\textwidth, alt={}, center]{8c6f9ac0-c24f-48d0-9fb2-883651e791d7-2_615_1312_1007_301}
\begin{enumerate}[label=(\alph*)]
\item State the times at which the velocity of the particle is zero.
\item Show that the particle travels a distance of 75 metres during the first 30 seconds of its motion.
\item Find the total distance travelled by the particle during the 50 seconds.
\item Find the distance of the particle from its initial position at the end of the 50 -second period.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2009 Q2 [10]}}