| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Sketch velocity-time graph |
| Difficulty | Standard +0.8 This is a multi-part SUVAT problem requiring students to set up equations from velocity-time graphs, use the equal-distance constraint to form a quadratic equation, and work through several interconnected calculations. While the individual techniques are standard M1 content, the problem requires careful coordination of multiple phases of motion and algebraic manipulation beyond routine exercises. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Graph with \(v\) on y-axis and \(t\) on x-axis, showing triangular shape with peak at time \(T\) between 0 and 80, with initial portion reaching 3.5 and final portion returning to 0.27 | B3 B3 | |
| (b) Areas under graphs equal: \(40(0.27) = 1.75(T + 80)\) | M1 A1 A1 | |
| \(6.25T = 140\); \(T = 22.4\) | M1 A1 | |
| (c) Area \(= 8T\), so distance \(= 179.2 \text{ m}\) | M1 A1 | |
| (d) \(\frac{3.5 + (80 - T)}{} = 0.0608 \text{ ms}^{-2}\) | M1 A1 | 15 marks |
(a) Graph with $v$ on y-axis and $t$ on x-axis, showing triangular shape with peak at time $T$ between 0 and 80, with initial portion reaching 3.5 and final portion returning to 0.27 | B3 B3 |
(b) Areas under graphs equal: $40(0.27) = 1.75(T + 80)$ | M1 A1 A1 |
$6.25T = 140$; $T = 22.4$ | M1 A1 |
(c) Area $= 8T$, so distance $= 179.2 \text{ m}$ | M1 A1 |
(d) $\frac{3.5 + (80 - T)}{} = 0.0608 \text{ ms}^{-2}$ | M1 A1 | 15 marks7. Two cyclists, Alice and Bobbie, travel from $P$ to $Q$ along a straight path. Alice starts from rest at $P$ just as Bobbie passes her at $3.5 \mathrm {~ms} ^ { - 1 }$. Bobbie continues at this speed while Alice accelerates at $0.2 \mathrm {~ms} ^ { - 2 }$ for $T$ seconds until she attains her maximum speed. At this moment both cyclists immediately start to slow down, with constant but different decelerations, and they come to rest at $Q 80$ seconds after Alice started moving.
\begin{enumerate}[label=(\alph*)]
\item Sketch, on the same diagram, the velocity-time graphs for the two cyclists.
By using the fact that both cyclists cover the same distance, find
\item the value of $T$,
\item the distance between $P$ and $Q$,
\item the magnitude of Bobbie's deceleration.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q7 [15]}}