| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | June |
| Marks | 10 |
| 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 M1 two-particle kinematics problem requiring a speed-time graph sketch and solving for when distances are equal. The setup is straightforward with constant accelerations, and the algebra involves equating distances using SUVAT equations—routine for M1 students with no novel insight required, making it slightly 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 |
3. A cyclist starts from rest at the point $O$ on a straight horizontal road. The cyclist moves along the road with constant acceleration $2 \mathrm {~ms} ^ { - 2 }$ for 4 seconds and then continues to move along the road at constant speed. At the instant when the cyclist stops accelerating, a motorcyclist starts from rest at the point $O$ and moves along the road with constant acceleration $4 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ in the same direction as the cyclist. The motorcyclist has been moving for $T$ seconds when she overtakes the cyclist.
\begin{enumerate}[label=(\alph*)]
\item Sketch, on the same axes, a speed-time graph for the motion of the cyclist and a speed-time graph for the motion of the motorcyclist, to the time when the motorcyclist overtakes the cyclist.
\item Find, giving your answer to 1 decimal place, the value of $T$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2018 Q3 [10]}}