| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| 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 | Standard +0.3 This is a standard three-stage SUVAT motion problem requiring students to apply kinematic equations systematically. While it involves algebraic manipulation with an unknown V and requires setting up equations from the total time and distance constraints, the problem follows a familiar M1 template with clear structure and straightforward application of v=u+at and area-under-graph methods. Slightly easier than average due to its predictable format. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Trapezium shape with line starting and finishing on \(t\)-axis | B1 | B1 for trapezium shape |
| \(V\) correctly marked on velocity axis | B1 (2) | B1 for \(V\) correctly marked |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(\frac{V}{t_1} = \frac{1}{2} \Rightarrow t_1 = 2V\) s; \(t_2 = 4V\) s | M1 A1; A1 | First A1 for \(V/0.5\) oe; Second A1 for \(V/0.25\) oe |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(t_3 = 300 - 2V - 4V = 300 - 6V\) s | M1 A1 (5) | Second M1 for \((300 - \text{sum of previous answers})\); allow 5 instead of 300 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(6300 = \frac{V(300 + 300 - 6V)}{2}\) or \(\frac{1}{2}(2V)(V) + (300-6V)(V) + \frac{1}{2}(4V)(V)\) | M1 A1 ft | M1 for using area = distance; A1 ft on answers in (b); must see \(\frac{1}{2}\) used at least once |
| \(V^2 - 100V + 2100 = 0\) | A1 | A1 for correct equation in form \(aV^2 + bV + c = 0\) |
| \((V-30)(V-70) = 0\) | M1 A1 | Second M1 for solving 3-term quadratic |
| \(V = 30\) or \(70\) | A1 for either 30 or 70 | |
| \(V = 30\ ({<}50)\) | A1 (6) |
## Question 7:
### Part (a):
| Working | Marks | Guidance |
|---------|-------|----------|
| Trapezium shape with line starting and finishing on $t$-axis | B1 | B1 for trapezium shape |
| $V$ correctly marked on velocity axis | B1 (2) | B1 for $V$ correctly marked |
### Part (b)(i)(ii):
| Working | Marks | Guidance |
|---------|-------|----------|
| $\frac{V}{t_1} = \frac{1}{2} \Rightarrow t_1 = 2V$ s; $t_2 = 4V$ s | M1 A1; A1 | First A1 for $V/0.5$ oe; Second A1 for $V/0.25$ oe |
### Part (b)(iii):
| Working | Marks | Guidance |
|---------|-------|----------|
| $t_3 = 300 - 2V - 4V = 300 - 6V$ s | M1 A1 (5) | Second M1 for $(300 - \text{sum of previous answers})$; allow 5 instead of 300 |
### Part (c):
| Working | Marks | Guidance |
|---------|-------|----------|
| $6300 = \frac{V(300 + 300 - 6V)}{2}$ or $\frac{1}{2}(2V)(V) + (300-6V)(V) + \frac{1}{2}(4V)(V)$ | M1 A1 ft | M1 for using area = distance; A1 ft on answers in (b); must see $\frac{1}{2}$ used at least once |
| $V^2 - 100V + 2100 = 0$ | A1 | A1 for correct equation in form $aV^2 + bV + c = 0$ |
| $(V-30)(V-70) = 0$ | M1 A1 | Second M1 for solving 3-term quadratic |
| $V = 30$ or $70$ | | A1 for either 30 or 70 |
| $V = 30\ ({<}50)$ | A1 (6) | |7. A train travels along a straight horizontal track between two stations, $A$ and $B$. The train starts from rest at $A$ and moves with constant acceleration $0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ until it reaches a speed of $V \mathrm {~ms} ^ { - 1 } , ( V < 50 )$. The train then travels at this constant speed before it moves with constant deceleration $0.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ until it comes to rest at $B$.
\begin{enumerate}[label=(\alph*)]
\item Sketch in the space below a speed-time graph for the motion of the train between the two stations $A$ and $B$.
The total time for the journey from $A$ to $B$ is 5 minutes.
\item Find, in terms of $V$, the length of time, in seconds, for which the train is
\begin{enumerate}[label=(\roman*)]
\item accelerating,
\item decelerating,
\item moving with constant speed.
Given that the distance between the two stations $A$ and $B$ is 6.3 km ,
\end{enumerate}\item find the value of $V$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2015 Q7 [13]}}