| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Two vehicles: overtaking or meeting (algebraic) |
| Difficulty | Moderate -0.3 This is a standard two-particle SUVAT problem requiring calculation of acceleration, sketching velocity-time graphs, and finding when vehicles meet by equating distances. While multi-part with several steps, it involves routine application of kinematic equations with no novel problem-solving insight required—slightly easier than average due to straightforward setup and clear methodology. |
| 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) \(\text{acc}^n = \frac{36-0}{9} = 4 \text{ ms}^{-2}\) | M1 A1 | |
| (b) [Graph showing speed vs time with car and motorbike curves] | B4 | |
| (c) after \(t\) seconds \(s_M = \frac{1}{2}(5)(30) + 30(t-5)\) (for \(t > 5\)) | M1 A1 | |
| after \(t\) seconds \(s_C = \frac{1}{2}(9)(36) + 36(t-9)\) (for \(t > 9\)) | M1 A1 | |
| car level with bike when \(s_M = s_C\) i.e. \(75 + 30t - 150 = 162 + 36t - 324\) | M2 | |
| \(t = 14.5\) seconds | A1 | (13) |
(a) $\text{acc}^n = \frac{36-0}{9} = 4 \text{ ms}^{-2}$ | M1 A1 |
(b) [Graph showing speed vs time with car and motorbike curves] | B4 |
(c) after $t$ seconds $s_M = \frac{1}{2}(5)(30) + 30(t-5)$ (for $t > 5$) | M1 A1 |
after $t$ seconds $s_C = \frac{1}{2}(9)(36) + 36(t-9)$ (for $t > 9$) | M1 A1 |
car level with bike when $s_M = s_C$ i.e. $75 + 30t - 150 = 162 + 36t - 324$ | M2 |
$t = 14.5$ seconds | A1 | (13) |5. A car and a motorbike are at rest adjacent to one another at a set of traffic lights on a long, straight stretch of road. They set off simultaneously at time $t = 0$. The motorcyclist accelerates uniformly at $6 \mathrm {~ms} ^ { - 2 }$ until he reaches a speed of $30 \mathrm {~ms} ^ { - 1 }$ which he then maintains. The car driver accelerates uniformly for 9 seconds until she reaches $36 \mathrm {~ms} ^ { - 1 }$ and then remains at this speed.
\begin{enumerate}[label=(\alph*)]
\item Find the acceleration of the car.
\item Draw on the same diagram speed-time graphs to illustrate the movements of both vehicles.
\item Find the value of $t$ when the car again draws level with the motorcyclist.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [13]}}