| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with velocity-time graph given |
| Difficulty | Moderate -0.8 This is a straightforward speed-time graph question testing standard M1 kinematics. Parts (a) and (b) involve routine calculations of acceleration (gradient) and distance (area under graph), plus sketching derived graphs. Part (c) requires setting up an algebraic expression for total distance and solving, but follows a predictable method. All techniques are core M1 content with no novel problem-solving required. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(i) \(\frac{7}{3} \text{ ms}^{-2}\), \(-\frac{7}{3} \text{ ms}^{-2}\), \(0 \text{ ms}^{-2}\) | B2 (–1 each error) | |
| (ii) \(45 \times 15 + \frac{1}{2} \times 35^2 = 1287.5 \text{ m}\) | M1 A1 | |
| (b)(i) Graph showing acceleration vs time | (ii) Graph showing displacement vs time (curved section from \(t=0\) to \(t=15\)) | |
| (c) \(15 \times 9T + 35 \times 3.5T = 3708\) | \(257.5T = 3708\) | \(T = 14.4\) |
(a)(i) $\frac{7}{3} \text{ ms}^{-2}$, $-\frac{7}{3} \text{ ms}^{-2}$, $0 \text{ ms}^{-2}$ | | B2 (–1 each error)
(ii) $45 \times 15 + \frac{1}{2} \times 35^2 = 1287.5 \text{ m}$ | | M1 A1
(b)(i) Graph showing acceleration vs time | (ii) Graph showing displacement vs time (curved section from $t=0$ to $t=15$) | | B2 B2
(c) $15 \times 9T + 35 \times 3.5T = 3708$ | $257.5T = 3708$ | $T = 14.4$ | M1 A1 M1 A1 | **12 marks**The diagram shows the speed-time graph for a particle during a period of $9T$ seconds.
\includegraphics{figure_6}
\begin{enumerate}[label=(\alph*)]
\item If $T = 5$, find
\begin{enumerate}[label=(\roman*)]
\item the acceleration for each section of the motion, [2 marks]
\item the total distance travelled by the particle. [2 marks]
\end{enumerate}
\item Sketch, for this motion,
\begin{enumerate}[label=(\roman*)]
\item an acceleration-time graph, [2 marks]
\item a displacement-time graph. [2 marks]
\end{enumerate}
\item Calculate the value of $T$ for which the distance travelled over the $9T$ seconds is 3.708 km. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q6 [12]}}