| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Sketch velocity-time graph |
| Difficulty | Moderate -0.3 This is a standard M1 SUVAT problem involving two particles with piecewise constant/uniformly accelerated motion. Students must recognize that equal journey times and distances give them two equations to solve for T. The sketch in part (a) is routine, and part (b) requires setting up distance equations using areas under speed-time graphs—a core M1 skill with no novel insight required. Slightly easier than average due to straightforward setup. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Notes |
| Correct shape for \(M\) | B1 | Must start and finish on axes |
| Figures \(40\) and \(T\) marked correctly | B1 | If delineators omitted B0 |
| Correct shape for \(N\) | B1 | Must start and finish on axes |
| Figures \(30\) and \(25\) marked correctly | B1 | N.B. If graphs do not cross and/or do not finish at same point, max score B1B1B0B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Notes |
| For \(N\): \(\frac{1}{2}(25 + 25 + t) \cdot 30 = 975\) OR \(\frac{1}{2}(25 + t_1) \cdot 30 = 975\) | M1 A1 | Using 975m for \(N\); equation in one unknown time |
| \(t = 15\), \(t_1 = 40\) | DM1 A1 | Dependent on first M; solving equation |
| For \(M\): \(\frac{1}{2}(25 + t + T) \cdot 40 = 975\) OR \(\frac{1}{2}(t_1 + T) \cdot 40 = 975\) | M1 A1 | Using 975m for \(M\); equation in \(T\) and possibly one other unknown |
| \(T = 8.75\) \(\left(8\frac{3}{4}\right.\) or \(\left.\frac{35}{4}\right)\) | DM1 A1 | Dependent on first, second and third M's; A1 for \(8.75\) or \(\frac{35}{4}\) or equivalent |
## Question 4:
### Part (a)
| Working | Marks | Notes |
|---------|-------|-------|
| Correct shape for $M$ | B1 | Must start and finish on axes |
| Figures $40$ and $T$ marked correctly | B1 | If delineators omitted B0 |
| Correct shape for $N$ | B1 | Must start and finish on axes |
| Figures $30$ and $25$ marked correctly | B1 | N.B. If graphs do not cross and/or do not finish at same point, max score B1B1B0B1 |
### Part (b)
| Working | Marks | Notes |
|---------|-------|-------|
| For $N$: $\frac{1}{2}(25 + 25 + t) \cdot 30 = 975$ OR $\frac{1}{2}(25 + t_1) \cdot 30 = 975$ | M1 A1 | Using 975m for $N$; equation in one unknown time |
| $t = 15$, $t_1 = 40$ | DM1 A1 | Dependent on first M; solving equation |
| For $M$: $\frac{1}{2}(25 + t + T) \cdot 40 = 975$ OR $\frac{1}{2}(t_1 + T) \cdot 40 = 975$ | M1 A1 | Using 975m for $M$; equation in $T$ and possibly one other unknown |
| $T = 8.75$ $\left(8\frac{3}{4}\right.$ or $\left.\frac{35}{4}\right)$ | DM1 A1 | Dependent on first, second and third M's; A1 for $8.75$ or $\frac{35}{4}$ or equivalent |4. Two trains $M$ and $N$ are moving in the same direction along parallel straight horizontal tracks. At time $t = 0 , M$ overtakes $N$ whilst they are travelling with speeds $40 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $30 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively. Train $M$ overtakes train $N$ as they pass a point $X$ at the side of the tracks.
After overtaking $N$, train $M$ maintains its speed of $40 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ for $T$ seconds and then decelerates uniformly, coming to rest next to a point $Y$ at the side of the tracks.
After being overtaken, train $N$ maintains its speed of $30 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ for 25 s and then decelerates uniformly, also coming to rest next to the point $Y$.
The times taken by the trains to travel between $X$ and $Y$ are the same.
\begin{enumerate}[label=(\alph*)]
\item Sketch, on the same diagram, the speed-time graphs for the motions of the two trains between $X$ and $Y$.
Given that $X Y = 975 \mathrm {~m}$,
\item find the value of $T$.\\
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2016 Q4 [12]}}