| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Session | Specimen |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Sketch velocity-time graph |
| Difficulty | Standard +0.8 This is a multi-stage kinematics problem requiring students to set up and solve simultaneous equations involving two different motion phases for each car, with the constraint that both reach the same point at the same time. While it uses standard SUVAT equations, the problem requires careful bookkeeping across multiple time intervals, translating the constraint into mathematical equations, and algebraic manipulation to find T. This goes beyond routine single-object SUVAT exercises and requires genuine problem-solving and coordination of information. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks |
|---|---|
| Shape (both) | B1 |
| Cross | B1 |
| Meet on \(t\)-axis | B1 |
| \(25, 20, 7, 25\) Figures | B1 |
| Answer | Marks |
|---|---|
| For \(Q\): \(20\left[\frac{t+25}{2}\right] = 800\) | M1 A1 |
| \(t = 55\) | DM1 A1 |
| For \(P\): \(25\left[\frac{T+55}{2}\right] = 800\) | M1 A1 |
| \(T = 9\) | DM1 A1 |
| solving for \(T\); |
## (a)
| Shape (both) | B1 |
| Cross | B1 |
| Meet on $t$-axis | B1 |
| $25, 20, 7, 25$ Figures | B1 |
**Total: (4)**
## (b)
For $Q$: $20\left[\frac{t+25}{2}\right] = 800$ | M1 A1 |
$t = 55$ | DM1 A1 |
For $P$: $25\left[\frac{T+55}{2}\right] = 800$ | M1 A1 |
$T = 9$ | DM1 A1 |
solving for $T$; | |
**Total: (8) [12]**Two cars $P$ and $Q$ are moving in the same direction along the same straight horizontal road. Car $P$ is moving with constant speed 25 m s$^{-1}$. At time $t = 0$, $P$ overtakes $Q$ which is moving with constant speed 20 m s$^{-1}$. From $t = 7$ seconds, $P$ decelerates uniformly, coming to rest at a point $X$ which is 800 m from the point where $P$ overtook $Q$. From $t = 25$ s, $Q$ decelerates uniformly, coming to rest at the same point $X$ at the same instant as $P$.
\begin{enumerate}[label=(\alph*)]
\item Sketch, on the same axes, the speed-time graphs of the two cars for the period from $t = 0$ to the time when they both come to rest at the point $X$.
[4]
\item Find the value of $T$.
[8]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [12]}}