| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Two-particle meeting or overtaking |
| Difficulty | Moderate -0.8 This is a straightforward kinematics problem requiring standard SUVAT equations for constant acceleration (P) and constant velocity (Q). Part (i) is direct formula application, and part (ii) involves setting distances equal and solving a quadratic equation—a routine M1 exercise with no conceptual challenges beyond textbook methods. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks |
|---|---|
| 6(i) | The distance travelled by P is |
| Answer | Marks | Guidance |
|---|---|---|
| The distance travelled by Q is 10t | B1 | |
| B1 | Accept 10t + 125 if used correctly below. | 2 |
| (ii) | Meet when 0.25t2=125+10t |
| Answer | Marks |
|---|---|
| Distance is 0.25×502=625 m | MM11 |
| Answer | Marks |
|---|---|
| A1 | All their wrong expressions for P and Q distances |
| Answer | Marks |
|---|---|
| [SC2 400 m seen] | 5 |
Question 6:
--- 6(i) ---
6(i) | The distance travelled by P is
0.5×0.5×t2
The distance travelled by Q is 10t | B1
B1 | Accept 10t + 125 if used correctly below. | 2
(ii) | Meet when 0.25t2=125+10t
so t2−40t−500=0
Solvinngg
t = 50 (or -10)
Distance is 0.25×502=625 m | MM11
F1
A1
A1 | All their wrong expressions for P and Q distances
Allow ± 125 or 125 omitted
Award for their expressions as long as one is
quadratic and one linear.
Must have 125 with correct sign.
Accept any method that yields (smaller) + ve root of
their 3 term quadratic
cao Allow –ve root not mentioned
cao
[SC2 400 m seen] | 5
7\includegraphics{figure_6}
Particles P and Q move in the same straight line. Particle P starts from rest and has a constant
acceleration towards Q of $0.5\text{ m s}^{-2}$. Particle Q starts 125 m from P at the same time and has a constant
speed of $10\text{ m s}^{-1}$ away from P. The initial values are shown in Fig. 4.
\begin{enumerate}[label=(\roman*)]
\item Write down expressions for the distances travelled by P and by Q at time $t$ seconds after the start
of the motion. [2]
\item How much time does it take for P to catch up with Q and how far does P travel in this time? [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M1 Q6 [7]}}