| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with all parameters given |
| Difficulty | Moderate -0.8 This is a straightforward kinematics problem using constant acceleration equations and speed-time graphs. All parts involve standard M1 techniques: sketching a trapezoid graph, calculating areas under the graph for distance, and applying suvat equations. The multi-part structure adds length but not conceptual difficulty—each step is routine for M1 students. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks |
|---|---|
| [Graph showing horizontal line at \(V = 5\) from 0 to 4, constant from 4 to 64, then decreasing linearly to 0 at 84] | B1 shape |
| B1 figs | |
| (2) |
| Answer | Marks |
|---|---|
| \((\frac{1}{2} \times 4 \times 5) + 60 \times 5\) | M1 A1 |
| \(= 310\) | A1 |
| (3) |
| Answer | Marks |
|---|---|
| \(\frac{(5 + V)}{2} \times 20 = (400-310)\) | M1 A2 ft |
| \(V = 4\) | DM1 A1 |
| (5) |
| Answer | Marks |
|---|---|
| \(\frac{5 - 4}{20} = 0.05 \text{ ms}^{-2}\) | M1 A1 |
| (2) | |
| 12 |
## (a)
[Graph showing horizontal line at $V = 5$ from 0 to 4, constant from 4 to 64, then decreasing linearly to 0 at 84] | B1 shape |
| | B1 figs |
| (2) |
## (b)
$(\frac{1}{2} \times 4 \times 5) + 60 \times 5$ | M1 A1 |
$= 310$ | A1 |
| (3) |
## (c)
$\frac{(5 + V)}{2} \times 20 = (400-310)$ | M1 A2 ft |
$V = 4$ | **DM1** A1 |
| (5) |
## (d)
$\frac{5 - 4}{20} = 0.05 \text{ ms}^{-2}$ | M1 A1 |
| (2) |
| **12** |
---A girl runs a 400 m race in a time of 84 s. In a model of this race, it is assumed that, starting from rest, she moves with constant acceleration for 4 s, reaching a speed of 5 m s$^{-1}$. She maintains this speed for 60 s and then moves with constant deceleration for 20 s, crossing the finishing line with a speed of $V$ m s$^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Sketch, in the space below, a speed-time graph for the motion of the girl during the whole race. [2]
\item Find the distance run by the girl in the first 64 s of the race. [3]
\item Find the value of $V$. [5]
\item Find the deceleration of the girl in the final 20 s of her race. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2011 Q4 [12]}}