| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Multi-phase journey: find unknown speed or time |
| Difficulty | Standard +0.3 This is a standard multi-stage SUVAT problem requiring systematic application of kinematic equations across three phases. Part (b) is straightforward (a = v/t), part (c) requires setting up a time equation (25 + t₂ + T = 150 where t₂ is found from v = u + at), and part (d) needs total distance divided by total time. While multi-step, each stage follows routine procedures with no conceptual challenges beyond careful bookkeeping, making it slightly easier than average. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct shape of \(v\)-\(t\) graph | B1 | Correct shape. Must be correct shape |
| Correct labels on axes: \(v\), \(t\) (or velocity, time), 6, 10, 25 and 150 need to be seen | B1 | |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(0.24\ (\text{m s}^{-2})\) | B1 | oe |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(T = 150 - 25 - T_1\) where \(T_1 = \frac{10-6}{0.05}\) | M1 | Complete method to find \(T\) |
| \(T = 45\) | A1 | |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(s = \frac{1}{2}(6)(25) + \frac{1}{2}(10+6)(T_1) + \frac{1}{2}(10)T\) | M1* | Complete method to find total distance travelled |
| Av. Speed \(= \frac{'940'}{150}\) | M1dep* | Divides their distance travelled by 150 |
| \(= 6.27\ (\text{m s}^{-1})\) | A1 | cao (oe e.g. exact answer is \(\frac{94}{15}\)) |
| [3] |
## Question 10:
### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct shape of $v$-$t$ graph | B1 | Correct shape. Must be correct shape |
| Correct labels on axes: $v$, $t$ (or velocity, time), 6, 10, 25 and 150 need to be seen | B1 | |
| **[2]** | | |
### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $0.24\ (\text{m s}^{-2})$ | B1 | oe |
| **[1]** | | |
### Part (c):
| Answer | Mark | Guidance |
|--------|------|----------|
| $T = 150 - 25 - T_1$ where $T_1 = \frac{10-6}{0.05}$ | M1 | Complete method to find $T$ |
| $T = 45$ | A1 | |
| **[2]** | | |
### Part (d):
| Answer | Mark | Guidance |
|--------|------|----------|
| $s = \frac{1}{2}(6)(25) + \frac{1}{2}(10+6)(T_1) + \frac{1}{2}(10)T$ | M1* | Complete method to find total distance travelled |
| Av. Speed $= \frac{'940'}{150}$ | M1dep* | Divides their distance travelled by 150 |
| $= 6.27\ (\text{m s}^{-1})$ | A1 | cao (oe e.g. exact answer is $\frac{94}{15}$) |
| **[3]** | | |
---10 A cyclist starts from rest and moves with constant acceleration along a straight horizontal road. The cyclist reaches a speed of $6 \mathrm {~ms} ^ { - 1 }$ in 25 seconds. The cyclist then moves with constant acceleration $0.05 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ until the speed is $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The cyclist then moves with constant deceleration until coming to rest. The total time for the cyclist's journey is 150 seconds.
\begin{enumerate}[label=(\alph*)]
\item Sketch a velocity-time graph to represent the cyclist's motion.
\item Find the acceleration during the first 25 seconds of the cyclist's motion.
The cyclist takes $T$ seconds to decelerate from $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ until coming to rest.
\item Determine the value of $T$.
\item Determine the average speed for the cyclist's journey.
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q10 [8]}}