| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| 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 straightforward kinematics problem using speed-time graphs. Part (a) requires a simple sketch, part (b) involves calculating area under the graph (trapezium formula) with one unknown, and part (c) is direct application of acceleration = change in velocity / time. All steps are routine M1 content with no problem-solving insight required, making it easier than average. |
| 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 |
|---|---|---|
| (a) Graph showing: straight line from (0, 25) to (4, V), then horizontal line from (4, V) to (12, t) | B1 (shape), B1 (figs) | 2 marks |
| (b) \(600 = 8V_1 + \frac{1}{2}(25 + V) \cdot 4\) \(\Rightarrow V = 55\) | M1 A1, A1 | 4 marks |
| (c) \(a = \frac{55 - 25}{4} = 7.5 \text{ m s}^{-2}\) | M1 A1 | 2 marks |
**(a)** Graph showing: straight line from (0, 25) to (4, V), then horizontal line from (4, V) to (12, t) | B1 (shape), B1 (figs) | 2 marks
**(b)** $600 = 8V_1 + \frac{1}{2}(25 + V) \cdot 4$ $\Rightarrow V = 55$ | M1 A1, A1 | 4 marks
**(c)** $a = \frac{55 - 25}{4} = 7.5 \text{ m s}^{-2}$ | M1 A1 | 2 marks
---A racing car is travelling on a straight horizontal road. Its initial speed is $25$ m s$^{-1}$ and it accelerates for $4$ s to reach a speed of $V$ m s$^{-1}$. It then travels at a constant speed of $V$ m s$^{-1}$ for a further $8$ s. The total distance travelled by the car during this $12$ s period is $600$ m.
\begin{enumerate}[label=(\alph*)]
\item Sketch a speed-time graph to illustrate the motion of the car during this $12$ s period. [2]
\item Find the value of $V$. [4]
\item Find the acceleration of the car during the initial $4$ s period. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q3 [8]}}