| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2017 |
| Session | June |
| Marks | 5 |
| Topic | Travel graphs |
| Type | Two-particle meeting or overtaking |
| Difficulty | Moderate -0.8 This is a standard kinematics problem involving constant velocity and constant acceleration with a delayed start. It requires setting up equations of motion (s = ut for the cyclist, s = ½at² for the bus) and solving a quadratic equation, but follows a well-practiced template with no conceptual surprises. Easier than average A-level due to straightforward setup and routine algebraic manipulation. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
**Question 10**
- $4(t + 5) = (0) + \dfrac{1}{2} \times \dfrac{1}{2} \times t^2$, where $t =$ time from bus setting off. **M1** ($s$ at constant $v$ for cyclist equated to $\ldots$)
- **A1** ($\ldots$ $s$ at constant $a$ for bus. Allow $t = 0$ as cyclist passes bus.)
- $\therefore t^2 - 16t - 80 = 0$
$\therefore (t - 20)(t + 4) = 0$ **M1** (Solve quadratic equation which must involve 3 non-zero terms.)
- $\therefore t = 20$ s (not $-4$) **A1** (cao. A0 if final answer contains both values of $t$. Note: $t = 0$ as cyclist passes bus gives $t = 25$ (and 1); must now subtract 5. SR If M0M0, allow B1 for $t = 20$ obtained without any wrong working, e.g. by trial and error.)
- $v = (0) + \dfrac{1}{2} \times 20 = 10\,\text{ms}^{-1}$ **B1** (FT *their* $t$.)
**Total: 5 marks**10 A cyclist travelling at a steady speed of $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ passes a bus which is at rest at a bus stop. 5 seconds later the bus sets off following the cyclist and accelerating at $\frac { 1 } { 2 } \mathrm {~m} \mathrm {~s} ^ { - 2 }$. How soon after setting off does the bus catch up with the cyclist? How fast is the bus going at this time?
{www.cie.org.uk} after the live examination series.
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\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2017 Q10 [5]}}