| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| 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 two-particle problem requiring sketching speed-time graphs, calculating times using constant acceleration equations, and comparing final speeds. While it involves multiple parts and careful bookkeeping across two particles, all techniques are routine applications of basic kinematics with no novel problem-solving insight required. Slightly easier than average due to straightforward setup and clear structure. |
| 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 |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Correct shape for A's graph (horizontal line at speed 4) | B1 | |
| Correct shape for B's graph: steeper gradient initially, must cross A's graph; both graphs end at same time | B1 | B0 if solid vertical line at end; if graphs on separate axes max B1B0B1 |
| 4 and \(T\) correctly marked on axes | B1 | Allow appropriate delineators; if no labels give BOD; if incorrect labels max B1B0B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{4}{0.8} = 5 \ \text{(s)}\) | B1 | Could be shown on graph |
| \(100 = \frac{(t + t - 5)}{2} \times 4\) OR \(100 = \frac{1}{2} \times 5 \times 4 + 4(t-5)\) | M1 A1ft | Attempt at equation in \(t\) only; trapezium or (rectangle \(+\) triangle) or (rectangle \(-\) triangle) oe; including \(\frac{1}{2}\) where appropriate; M0 for single suvat for whole motion; A1ft correct equation in \(t\) only ft on their 5 |
| \(t = 27.5 \ \text{(s)}\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(100 = \frac{(27.5 + 27.5 - T)}{2} \times T\) OR \(100 = \frac{1}{2} \times T \times T + T(27.5 - T)\) | M1 A1ft | Attempt at equation in \(T\) only; correct structure; M0 for single suvat for whole motion; A1ft correct equation ft on their 27.5 |
| \(T^2 - 55T + 200 = 0\) oe | A1 | Correct 3-term quadratic |
| \(T = 3.915047\ldots\) accept 3.9 or better | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(4 - 3.915\ldots\) (Allow \(T - 4\)) | M1 | |
| \(0.085\) or better \((\text{ms}^{-1})\) | A1ft | Follow through on their \(T\) value provided it's \(< 4\); must be correct to at least 2 SF |
## Question 7:
### Part 7(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Correct shape for A's graph (horizontal line at speed 4) | B1 | |
| Correct shape for B's graph: steeper gradient initially, must cross A's graph; both graphs end at same time | B1 | B0 if solid vertical line at end; if graphs on separate axes max B1B0B1 |
| 4 and $T$ correctly marked on axes | B1 | Allow appropriate delineators; if no labels give BOD; if incorrect labels max B1B0B1 |
### Part 7(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{4}{0.8} = 5 \ \text{(s)}$ | B1 | Could be shown on graph |
| $100 = \frac{(t + t - 5)}{2} \times 4$ **OR** $100 = \frac{1}{2} \times 5 \times 4 + 4(t-5)$ | M1 A1ft | Attempt at equation in $t$ only; trapezium or (rectangle $+$ triangle) or (rectangle $-$ triangle) oe; including $\frac{1}{2}$ where appropriate; M0 for single suvat for whole motion; A1ft correct equation in $t$ only ft on their 5 |
| $t = 27.5 \ \text{(s)}$ | A1 | cao |
### Part 7(c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $100 = \frac{(27.5 + 27.5 - T)}{2} \times T$ **OR** $100 = \frac{1}{2} \times T \times T + T(27.5 - T)$ | M1 A1ft | Attempt at equation in $T$ only; correct structure; M0 for single suvat for whole motion; A1ft correct equation ft on their 27.5 |
| $T^2 - 55T + 200 = 0$ oe | A1 | Correct 3-term quadratic |
| $T = 3.915047\ldots$ accept 3.9 or better | A1 | cao |
### Part 7(d):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $4 - 3.915\ldots$ (Allow $T - 4$) | M1 | |
| $0.085$ or better $(\text{ms}^{-1})$ | A1ft | Follow through on their $T$ value provided it's $< 4$; must be correct to at least **2 SF** |7. Two small children, Ajaz and Beth, are running a 100 m race along a straight horizontal track. They both start from rest, leaving the start line at the same time.
Ajaz accelerates at $0.8 \mathrm {~ms} ^ { - 2 }$ up to a speed of $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and then maintains this speed until he crosses the finish line.
Beth accelerates at $1 \mathrm {~ms} ^ { - 2 }$ for $T$ seconds and then maintains a constant speed until she crosses the finish line.
Ajaz and Beth cross the finish line at the same time.
\begin{enumerate}[label=(\alph*)]
\item Sketch, on the same axes, a speed-time graph for each child, from the instant when they leave the start line to the instant when they cross the finish line.
\item Find the time taken by Ajaz to complete the race.
\item Find the value of $T$
\item Find the difference in the speeds of the two children as they cross the finish line.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2022 Q7 [13]}}