| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with algebraic unknowns |
| Difficulty | Moderate -0.8 This is a standard M1 kinematics question with straightforward unit conversion, sketch, and trapezium area calculation. Part (a) is routine conversion, part (b) is basic sketching, and part (c) requires setting up equations from the speed-time graph area but involves no novel problem-solving—just systematic application of SUVAT principles and area under graph. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks |
|---|---|
| \(108 \times 1000/3600 = 30 \text{ m s}^{-1}\) | M1 A1 (2) |
| Answer | Marks |
|---|---|
| Trapezium (B0 for triangle), from the origin, finishing on the \(t\)-axis. | B1 shape |
| Second dependent B1 ft on their '30' and 480 or 108 and (\(8/60\) oe). | DB1 ft figs (2) |
| Answer | Marks |
|---|---|
| \(12000 = \frac{1}{2} \times 30(480 + 480 - 4T)\) | M1 A2 |
| \(T = 40\) | A1 |
| \(a = 30/40 = 0.75 \text{ m s}^{-2}\) | M1 A1 (6) |
## Part (a)
$108 \times 1000/3600 = 30 \text{ m s}^{-1}$ | M1 A1 (2) |
## Part (b)
Trapezium (B0 for triangle), from the origin, finishing on the $t$-axis. | B1 shape |
Second dependent B1 ft on their '30' and 480 or 108 and ($8/60$ oe). | DB1 ft figs (2) |
## Part (c)
$12000 = \frac{1}{2} \times 30(480 + 480 - 4T)$ | M1 A2 |
$T = 40$ | A1 |
$a = 30/40 = 0.75 \text{ m s}^{-2}$ | M1 A1 (6) |
**Notes for Question 7(a):**
M1 for $108 \times 1000/3600$ oe
A1 for $30$
**Notes for Question 7(b):**
First B1 for trapezium (B0 for triangle), from the origin, finishing on the $t$-axis.
Second dependent B1 ft on their '30' and 480 or 108 and ($8/60$ oe).
**Notes for Question 7(c):**
First M1 for clear attempt at equating total area under a trapezium to distance travelled oe (equation must include at least one '1/2') to give equation in ONE unknown.
A2 for a correct equation , -1 each error. N.B. Repeated use of an incorrect $v$ from part (a) is ONE error.
Third A1 for $T = 40$ (or 120)
N.B. (First M1 only for $\frac{1}{2}(480 + x).30 = 12000$
First A1 for $480 - x = 160$; Second A1 if they divide 160 in ratio 1:3)
(First M0 if they use $s$ = the full distance in any single suvat equation)
Second M1 (independent) for a complete method to find $a$.
Fourth A1 for $0.75$
---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 until it reaches its maximum speed of 108 km h$^{-1}$. The train then travels at this speed before it moves with constant deceleration coming to rest at $B$. The journey from $A$ to $B$ takes 8 minutes.
\begin{enumerate}[label=(\alph*)]
\item Change 108 km h$^{-1}$ into m s$^{-1}$. [2]
\item Sketch a speed-time graph for the motion of the train between the two stations $A$ and $B$. [2]
\end{enumerate}
Given that the distance between the two stations is 12 km and that the time spent decelerating is three times the time spent accelerating,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the acceleration, in m s$^{-2}$, of the train. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2015 Q7 [10]}}