| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| 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 using speed-time graphs with constant acceleration. Part (a) requires sketching a trapezoid graph from given information. Part (b) involves setting up equations using area under the graph equals distance and total time, then solving simultaneously—routine application of SUVAT principles with no conceptual challenges beyond textbook exercises. |
| 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 |
|---|---|---|
| First two line segments | B1 | (3) |
| Third line segment | B1 | |
| 8, 75 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{2} \times 8 \times (T + 75) = 500\) | M1 A2 (1,0) | |
| Solving to \(T = 50\) | DM1 A1 | (5) [8] |
**Part (a):**
First two line segments | B1 | (3)
Third line segment | B1 |
8, 75 | B1 |
**Part (b):**
$\frac{1}{2} \times 8 \times (T + 75) = 500$ | M1 A2 (1,0) |
Solving to $T = 50$ | DM1 A1 | (5) [8]An athlete runs along a straight road. She starts from rest and moves with constant acceleration for 5 seconds, reaching a speed of 8 m s$^{-1}$. This speed is then maintained for $T$ seconds. She then decelerates at a constant rate until she stops. She has run a total of 500 m in 75 s.
\begin{enumerate}[label=(\alph*)]
\item In the space below, sketch a speed-time graph to illustrate the motion of the athlete. [3]
\item Calculate the value of $T$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2010 Q2 [8]}}