| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Sketch velocity-time graph |
| Difficulty | Moderate -0.8 This is a straightforward M1 SUVAT question with all parameters explicitly given. Parts (a)(i-iv) involve routine sketching, calculating distance from a velocity-time graph (trapezium areas), finding average speed, and comparing given accelerations. Part (b) requires basic interpretation of curved vs straight-line graphs. All steps are standard textbook exercises with no problem-solving insight required—easier than average A-level maths. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| [velocity-time graph with 3 straight lines] | B1, B1, B1 | Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(s = \frac{1}{2}\times10\times4 + \frac{1}{2}\times(4+12)\times10 + \frac{1}{2}(12+16)\times10\) | M1, m1, A1 | area attempt, full method, equation correct |
| \(s = 240\) metres | A1\(\sqrt{}\) | Total: 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Average speed \(= \frac{240}{30}\) | M1 | |
| \(= 8 \text{ ms}^{-1}\) | A1\(\sqrt{}\) | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Greatest acceleration \(= 2^{\text{nd}}\) stage | ||
| \(= \frac{12-4}{10}\) | M1 | |
| \(= 0.8 \text{ ms}^{-2}\) | A1 | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Less | B1 | |
| area below curve \(<\) area below line / velocity lower | B1 | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Change in velocity more gradual | B1 | Total: 1 |
## Question 6:
### Part (a)(i)
| Working | Marks | Guidance |
|---------|-------|----------|
| [velocity-time graph with 3 straight lines] | B1, B1, B1 | Total: 3 | 3 straight lines; correct end points; sensible scales + labelled $v/t$ |
### Part (a)(ii)
| Working | Marks | Guidance |
|---------|-------|----------|
| $s = \frac{1}{2}\times10\times4 + \frac{1}{2}\times(4+12)\times10 + \frac{1}{2}(12+16)\times10$ | M1, m1, A1 | area attempt, full method, equation correct | Or: equation attempted, full method, all correct |
| $s = 240$ metres | A1$\sqrt{}$ | Total: 4 | $\sqrt{}$ one slip |
### Part (a)(iii)
| Working | Marks | Guidance |
|---------|-------|----------|
| Average speed $= \frac{240}{30}$ | M1 | |
| $= 8 \text{ ms}^{-1}$ | A1$\sqrt{}$ | Total: 2 | $\sqrt{}$ distance |
### Part (a)(iv)
| Working | Marks | Guidance |
|---------|-------|----------|
| Greatest acceleration $= 2^{\text{nd}}$ stage | | |
| $= \frac{12-4}{10}$ | M1 | |
| $= 0.8 \text{ ms}^{-2}$ | A1 | Total: 2 | cao |
### Part (b)(i)
| Working | Marks | Guidance |
|---------|-------|----------|
| Less | B1 | |
| area below curve $<$ area below line / velocity lower | B1 | Total: 2 | no additional incorrect statements |
### Part (b)(ii)
| Working | Marks | Guidance |
|---------|-------|----------|
| Change in velocity more gradual | B1 | Total: 1 | |
---6 A van moves from rest on a straight horizontal road.
\begin{enumerate}[label=(\alph*)]
\item In a simple model, the first 30 seconds of the motion are represented by three separate stages, each lasting 10 seconds and each with a constant acceleration.
During the first stage, the van accelerates from rest to a velocity of $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
During the second stage, the van accelerates from $4 \mathrm {~ms} ^ { - 1 }$ to $12 \mathrm {~ms} ^ { - 1 }$.\\
During the third stage, the van accelerates from $12 \mathrm {~ms} ^ { - 1 }$ to $16 \mathrm {~ms} ^ { - 1 }$.
\begin{enumerate}[label=(\roman*)]
\item Sketch a velocity-time graph to represent the motion of the van during the first 30 seconds of its motion.
\item Find the total distance that the van travels during the 30 seconds.
\item Find the average speed of the van during the 30 seconds.
\item Find the greatest acceleration of the van during the 30 seconds.
\end{enumerate}\item In another model of the 30 seconds of the motion, the acceleration of the van is assumed to vary during the first and third stages of the motion, but to be constant during the second stage, as shown in the velocity-time graph below.\\
\includegraphics[max width=\textwidth, alt={}, center]{c220e6c4-2676-4022-8301-7d720dc082b2-5_554_1138_1432_539}
The velocity of the van takes the same values at the beginning and the end of each stage of the motion as in part (a).
\begin{enumerate}[label=(\roman*)]
\item State, with a reason, whether the distance travelled by the van during the first 10 seconds of the motion in this model is greater or less than the distance travelled during the same time interval in the model in part (a).
\item Give one reason why this model represents the motion of the van more realistically than the model in part (a).
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA M1 2006 Q6 [16]}}