| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Displacement expressions and comparison |
| Difficulty | Moderate -0.3 This is a standard two-particle SUVAT problem requiring students to set up distance equations and solve when they're equal. While it involves multiple steps (writing expressions, setting equal, solving quadratic), it's a textbook exercise with no novel insight required—slightly easier than average due to straightforward setup and clean numbers. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Distance travelled by P is \(0.5\times0.5\times t^2\) | B1 | |
| Distance travelled by Q is \(10t\) | B1 | Accept \(10t + 125\) if used correctly below |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Meet when \(0.25t^2 = 125 + 10t\) | M1 | Allow their wrong expressions for P and Q distances |
| F1 | Award for their expressions as long as one is quadratic and one linear. Must have 125 with correct sign | |
| so \(t^2 - 40t - 500 = 0\) | ||
| Solving | M1 | Accept any method that yields (smaller) \(+\)ve root of their 3 term quadratic |
| \(t = 50\) (or \(-10\)) | A1 | cao. Allow \(-\)ve root not mentioned |
| Distance is \(0.25\times50^2 = 625\) m | A1 | cao. SC2 400 m seen |
# Question 4:
## Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Distance travelled by P is $0.5\times0.5\times t^2$ | B1 | |
| Distance travelled by Q is $10t$ | B1 | Accept $10t + 125$ if used correctly below |
## Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Meet when $0.25t^2 = 125 + 10t$ | M1 | Allow their wrong expressions for P and Q distances |
| | F1 | Award for their expressions as long as one is quadratic and one linear. Must have 125 with correct sign |
| so $t^2 - 40t - 500 = 0$ | | |
| Solving | M1 | Accept any method that yields (smaller) $+$ve root of their 3 term quadratic |
| $t = 50$ (or $-10$) | A1 | cao. Allow $-$ve root not mentioned |
| Distance is $0.25\times50^2 = 625$ m | A1 | cao. SC2 400 m seen |
---4
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{170edb27-324e-44df-8dc1-7d8fbad680fe-3_346_981_781_584}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{center}
\end{figure}
Particles P and Q move in the same straight line. Particle P starts from rest and has a constant acceleration towards Q of $0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. Particle Q starts 125 m from P at the same time and has a constant speed of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ away from P . The initial values are shown in Fig. 4.\\
(i) Write down expressions for the distances travelled by P and by Q at time $t$ seconds after the start of the motion.\\
(ii) How much time does it take for P to catch up with Q and how far does P travel in this time?
\hfill \mbox{\textit{OCR MEI M1 2008 Q4 [7]}}