CAIE M1 2019 June — Question 1 5 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2019
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConstant acceleration (SUVAT)
TypeMulti-phase journey: find total distance
DifficultyEasy -1.2 This is a straightforward SUVAT application with clearly defined stages and all parameters given. Students simply apply v=u+at for each stage, sketch the trapezoid, and calculate area. It requires only routine recall of basic kinematics formulas with no problem-solving insight or algebraic manipulation.
Spec3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae

1 A bus moves in a straight line between two bus stops. The bus starts from rest and accelerates at \(2.1 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for 5 s . The bus then travels for 24 s at constant speed and finally slows down, with a constant deceleration, stopping in a further 6 s . Sketch a velocity-time graph for the motion and hence find the distance between the two bus stops.

Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
TrapeziumB1 Includes \((0,0)\) and \((...,0)\)
\((t=0),\ t=5,\ t=29,\ t=35\)B1 Correct trapezium with key time values
\(v_{max} = 2.1 \times 5 = 10.5\ \text{ms}^{-1}\)B1
\([\frac{1}{2} \times (24+35) \times 10.5]\) or \([\frac{1}{2} \times 5 \times 10.5 + 24 \times 10.5 + \frac{1}{2} \times 6 \times 10.5]\)M1 Use of area property to find distance
\(309.75\ \text{m}\) or \(310\ \text{m}\)A1
5
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Trapezium | **B1** | Includes $(0,0)$ and $(...,0)$ |
| $(t=0),\ t=5,\ t=29,\ t=35$ | **B1** | Correct trapezium with key time values |
| $v_{max} = 2.1 \times 5 = 10.5\ \text{ms}^{-1}$ | **B1** | |
| $[\frac{1}{2} \times (24+35) \times 10.5]$ or $[\frac{1}{2} \times 5 \times 10.5 + 24 \times 10.5 + \frac{1}{2} \times 6 \times 10.5]$ | **M1** | Use of area property to find distance |
| $309.75\ \text{m}$ or $310\ \text{m}$ | **A1** | |
| | **5** | |

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1 A bus moves in a straight line between two bus stops. The bus starts from rest and accelerates at $2.1 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ for 5 s . The bus then travels for 24 s at constant speed and finally slows down, with a constant deceleration, stopping in a further 6 s . Sketch a velocity-time graph for the motion and hence find the distance between the two bus stops.

\hfill \mbox{\textit{CAIE M1 2019 Q1 [5]}}