| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2010 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Two-particle meeting or overtaking |
| Difficulty | Standard +0.3 This is a standard M1 kinematics problem involving two vehicles with different motion profiles meeting at the same point. While it requires careful setup of equations using suvat and area under speed-time graphs, the problem-solving approach is routine for M1 students. The 12 marks reflect length rather than conceptual difficulty—it's slightly easier than average A-level questions overall due to being methodical rather than requiring insight. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks |
|---|---|
| Shape (both) | B1 |
| Cross | B1 |
| Meet on \(t\)-axis | B1 |
| Figures 25, 20, T, 25 | B1 |
| [4] |
| 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 |
| solving for \(T\); \(T = 9\) | DM1 A1 |
| [8] | |
| [12] |
## Part (a)
Shape (both) | B1 |
Cross | B1 |
Meet on $t$-axis | B1 |
Figures 25, 20, T, 25 | B1 |
| [4] |
## Part (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 |
solving for $T$; $T = 9$ | DM1 A1 |
| [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 $t = T$ 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 2010 Q5 [12]}}