| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 11 |
| 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 involving constant acceleration in three phases. Part (a) requires sketching a trapezoid velocity-time graph with given algebraic expressions. Part (b) uses the area under the graph to form an equation (routine application of distance = area under v-t graph). Part (c) solves a quadratic equation. All steps are textbook-standard with no novel insight required, making it easier than average, though the algebraic manipulation with parameter x adds minor complexity compared to purely numerical questions. |
| Spec | 3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Velocity-time graph with axes labeled, trapezium shape with height \(5x\), horizontal section from \(t=2x\) to \(t=12g\), sloped sections reaching \(t=20x\) | B2 graph; B2 labelling | |
| (b) Area = \(\frac{1}{2} \times 5x(20x + 126 - 2x) = 45x^2 + 315x = 5400\) (given) | M1 M1 A1 | |
| \(\div 45: x^2 + 7x = 120\) | A1 | |
| (c) \(x^2 + 7x - 120 = 0\) giving \((x-8)(x+15) = 0\) so \(x = 8\) | M1 A1 A1 | total: 11 |
(a) Velocity-time graph with axes labeled, trapezium shape with height $5x$, horizontal section from $t=2x$ to $t=12g$, sloped sections reaching $t=20x$ | B2 graph; B2 labelling |
(b) Area = $\frac{1}{2} \times 5x(20x + 126 - 2x) = 45x^2 + 315x = 5400$ (given) | M1 M1 A1 |
$\div 45: x^2 + 7x = 120$ | A1 |
(c) $x^2 + 7x - 120 = 0$ giving $(x-8)(x+15) = 0$ so $x = 8$ | M1 A1 A1 | total: 11A train starts from rest at a station $S$ and accelerates at a constant rate for $2x$ seconds to a speed of $5x$ ms$^{-1}$. It maintains this speed until 126 seconds after it left $S$ and then decelerates at a constant rate until it comes to rest at another station $T$, $20x$ seconds after it left $S$.
\begin{enumerate}[label=(\alph*)]
\item Sketch a velocity-time graph for this journey. [4 marks]
\end{enumerate}
Given that the distance between $S$ and $T$ is $5.4$ km,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item show that $x^2 + 7x = 120$. [4 marks]
\item Find the value of $x$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [11]}}