| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Multi-phase journey: find unknown speed or time |
| Difficulty | Moderate -0.3 This is a standard M1 SUVAT question with multiple stages requiring systematic application of kinematic equations. While it involves several phases and algebraic manipulation with an unknown V, each step follows routine procedures: using s=½(u+v)t to find V from the given distance, then applying SUVAT formulae to each subsequent stage. The multi-stage nature adds length but not conceptual difficulty—it's slightly easier than average due to being a textbook-style structured problem with clear signposting. |
| Spec | 3.02b 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 |
| Shape of graph for \(0 \leq t \leq 50\) | B1 | |
| Shape of graph for \(t > 50\) | B1 | |
| Values \(V, 8, 15, 20, 30\) appropriately used | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(140 = \frac{1}{2} \times 20 \times V\) | M1 | Use of area under graph (must have '\(\frac{1}{2}\)') or suvat to obtain equation in \(V\) only |
| \(V = 14\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(8 = V - \frac{1}{3}t_1\) and/or \(0 = 8 - \frac{1}{3}t_2\) | M1 | First M1 for use of either equation |
| \(t_1 = 12\), (and/or \(t_2 = 24\)) | A1 | First A1 for either value |
| Total time \(= 20 + 30 + t_1 + 15 + t_2 = 101\) (seconds) | DM1 A1 | Second M1 dependent on first M1; must include all 5 time intervals |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Total distance \(= 140 + 30V + \frac{V+8}{2}t_1 + 15\times 8 + \frac{1}{2}\times 8 \times t_2\) | M1A2ft | First M1 for expression including all parts of motion; where triangle or trapezium used a '\(\frac{1}{2}\)' must be seen. A2 ft on \(V\), \(t_1\), \(t_2\) (−1 each error) |
| \(= 140 + 30\times14 + 11\times12 + 15\times8 + 24\times4\) | ||
| \(= 908\ \text{(m)}\) | A1 |
# Question 3:
## Part (a)
| Working | Marks | Guidance |
|---------|-------|----------|
| Shape of graph for $0 \leq t \leq 50$ | B1 | |
| Shape of graph for $t > 50$ | B1 | |
| Values $V, 8, 15, 20, 30$ appropriately used | B1 | |
## Part (b)
| Working | Marks | Guidance |
|---------|-------|----------|
| $140 = \frac{1}{2} \times 20 \times V$ | M1 | Use of area under graph (must have '$\frac{1}{2}$') or suvat to obtain equation in $V$ only |
| $V = 14$ | A1 | |
## Part (c)
| Working | Marks | Guidance |
|---------|-------|----------|
| $8 = V - \frac{1}{3}t_1$ and/or $0 = 8 - \frac{1}{3}t_2$ | M1 | First M1 for use of either equation |
| $t_1 = 12$, (and/or $t_2 = 24$) | A1 | First A1 for either value |
| Total time $= 20 + 30 + t_1 + 15 + t_2 = 101$ (seconds) | DM1 A1 | Second M1 dependent on first M1; must include all 5 time intervals |
## Part (d)
| Working | Marks | Guidance |
|---------|-------|----------|
| Total distance $= 140 + 30V + \frac{V+8}{2}t_1 + 15\times 8 + \frac{1}{2}\times 8 \times t_2$ | M1A2ft | First M1 for expression including all parts of motion; where triangle or trapezium used a '$\frac{1}{2}$' must be seen. A2 ft on $V$, $t_1$, $t_2$ (−1 each error) |
| $= 140 + 30\times14 + 11\times12 + 15\times8 + 24\times4$ | | |
| $= 908\ \text{(m)}$ | A1 | |
---3. A car starts from rest and moves with constant acceleration along a straight horizontal road. The car reaches a speed of $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in 20 seconds. It moves at constant speed $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$ for the next 30 seconds, then moves with constant deceleration $\frac { 1 } { 2 } \mathrm {~m} \mathrm {~s} ^ { - 2 }$ until it has speed $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. It moves at speed $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ for the next 15 seconds and then moves with constant deceleration $\frac { 1 } { 3 } \mathrm {~m} \mathrm {~s} ^ { - 2 }$ until it comes to rest.
\begin{enumerate}[label=(\alph*)]
\item Sketch, in the space below, a speed-time graph for this journey.
In the first 20 seconds of this journey the car travels 140 m .
Find
\item the value of $V$,
\item the total time for this journey,
\item the total distance travelled by the car.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2014 Q3 [13]}}