| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Sketch velocity-time graph |
| Difficulty | Easy -1.2 This is a straightforward multi-stage SUVAT question with all parameters explicitly given. Part (a) is a simple one-step calculation using v=u+at, part (b) is a routine sketch, part (c) requires finding areas under the velocity-time graph (basic trapezium calculation), and part (d) asks for a standard modelling criticism. No problem-solving insight or novel application is required—purely procedural application of standard M1 techniques. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(v = u + at\) | ||
| \(0 = 10 + (-0.8) \times t\) | M1 | Full method with \(u\), \(v\) used correctly; accept \(\pm 0.8\) |
| \(t = 12.5\) sec | A1 | CAO (correct subs and answer) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Velocity-time graph with correct shape | B1, B1, B1 | Each line straight and correct end points |
| Axes labelled \(v\), \(t\) | B1 | SC: B1 for 3 lines giving correct shape but no values shown; SC: first error in labelling times loses B1, repeated errors no further penalty |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| distance \(= \frac{1}{2} \times 10 \times (4 + 22.5)\) | M1 | Full correct method |
| A1F | Correct subs, FT graph if final \(t = 12.5\) | |
| \(= 132.5\) metres | A1F | FT one slip, AWRT 133 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Acceleration unlikely to change so abruptly or be constant, or velocity unlikely to be constant | B1 |
## Question 3:
### Part (a)
| Working | Marks | Guidance |
|---------|-------|----------|
| $v = u + at$ | | |
| $0 = 10 + (-0.8) \times t$ | M1 | Full method with $u$, $v$ used correctly; accept $\pm 0.8$ |
| $t = 12.5$ sec | A1 | CAO (correct subs and answer) | **Total: 2** |
### Part (b)
| Working | Marks | Guidance |
|---------|-------|----------|
| Velocity-time graph with correct shape | B1, B1, B1 | Each line straight and correct end points |
| Axes labelled $v$, $t$ | B1 | SC: B1 for 3 lines giving correct shape but no values shown; SC: first error in labelling times loses B1, repeated errors no further penalty | **Total: 4** |
### Part (c)
| Working | Marks | Guidance |
|---------|-------|----------|
| distance $= \frac{1}{2} \times 10 \times (4 + 22.5)$ | M1 | Full correct method |
| | A1F | Correct subs, FT graph if final $t = 12.5$ |
| $= 132.5$ metres | A1F | FT one slip, AWRT 133 | **Total: 3** |
### Part (d)
| Working | Marks | Guidance |
|---------|-------|----------|
| Acceleration unlikely to change so abruptly or be constant, or velocity unlikely to be constant | B1 | | **Total: 1** |
---3 A car travels along a straight horizontal road. The motion of the car can be modelled as three separate stages.
During the first stage, the car accelerates uniformly from rest to a velocity of $10 \mathrm {~ms} ^ { - 1 }$ in 6 seconds.
During the second stage, the car travels with a constant velocity of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ for a further 4 seconds.
During the third stage of the motion, the car travels with a uniform retardation of magnitude $0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ until it comes to rest.
\begin{enumerate}[label=(\alph*)]
\item Show that the time taken for the third stage of the motion is 12.5 seconds.
\item Sketch a velocity-time graph for the car during the three stages of the motion.
\item Find the total distance travelled by the car during the motion.
\item State one criticism of the model of the motion.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2006 Q3 [10]}}