| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Topic | Travel graphs |
| Type | Multi-stage motion with all parameters given |
| Difficulty | Moderate -0.8 This is a straightforward kinematics problem with all parameters given explicitly. Students apply standard SUVAT equations in a routine three-part structure: sketch a trapezoid velocity-time graph, calculate v = u + at and s = ut + ½at², then use areas under the graph to find total time. No problem-solving insight or novel approach required—purely procedural application of basic mechanics formulas. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
**Question 8**
**(i)** [Trapezium shape: middle portion horizontal, one vertex at origin, fourth vertex on the $t$ axis.]
— B1: Trapezium (middle portion horizontal), one vertex at the origin, fourth vertex on the $t$ axis. B1: Third part steeper than first. Axes labelled $t$ and $v$. **[2]**
**(ii)** At the end of the first 16 seconds:
$v_1 = (0+)\ 0.5 \times 16 = 8\ \text{ms}^{-1}$
$s_1 = \frac{1}{2}(0 + 8) \times 16 = 64\ \text{m}$
or $(0+)\ \frac{1}{2} \times 0.5 \times 16^2$
— B1: Gradient of first line or 'suvat'. B1: Area of LH triangle or 'suvat'. **[2]**
**(iii)** When slowing down:
$0 = 8 - 1 \times t_3 \quad \therefore t_3 = 8\ \text{s}$
— B1: Gradient of third line or 'suvat'. Ft *their* $v_1$.
$s_3 = \frac{1}{2}(8 + 0) \times 8 = 32\ \text{m}$
— B1: Area of RH triangle or 'suvat'. Ft *their* $v_1$ and/or $t_3$.
At constant speed:
$s_2 = 300 - (64 + 32) = 204\ \text{m}$
$t_2 = 204/8 = 25.5\ \text{s}$
$\therefore$ Total time $= 16 + 25.5 + 8 = 49.5\ \text{s}$
— M1: Use area of rectangle $\ldots$ A1: $\ldots$ to find the time. Ft *their* $v_1$ and/or $t_3$. A1: A.G. Shown convincingly. **[5]**8 A tram travels from stop $A$ to stop $B$, a distance of 300 m . First the tram starts from rest at $A$ and accelerates uniformly at $0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ for 16 seconds. Then it travels at a constant speed and finally it slows down uniformly at $1 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ coming to rest at $B$.\\
(i) Sketch the velocity-time graph for the journey of the tram from $A$ to $B$.\\
(ii) Find the speed of the tram and the distance travelled at the end of the first 16 seconds.\\
(iii) Show that the journey from $A$ to $B$ takes 49.5 seconds.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2015 Q8 [5]}}