AQA Paper 2 2018 June — Question 15 9 marks

Exam BoardAQA
ModulePaper 2 (Paper 2)
Year2018
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVariable acceleration (1D)
TypeVariable acceleration with initial conditions
DifficultyStandard +0.8 This question requires integrating acceleration twice to find displacement, then solving a non-standard equation (involving t^4 and t^5 terms) numerically. While the setup is straightforward mechanics, solving these equations requires either iterative methods or calculator techniques beyond routine A-level procedures, and part (c) tests conceptual understanding of mathematical modelling assumptions.
Spec3.02d Constant acceleration: SUVAT formulae3.02f Non-uniform acceleration: using differentiation and integration
A driver is road-testing two minibuses, A and B, for a taxi company. The performance of each minibus along a straight track is compared. A flag is dropped to indicate the start of the test. Each minibus starts from rest. The acceleration in m s\(^{-2}\) of each minibus is modelled as a function of time, \(t\) seconds, after the flag is dropped: The acceleration of A = \(0.138 t^2\) The acceleration of B = \(0.024 t^3\)
  1. Find the time taken for A to travel 100 metres. Give your answer to four significant figures. [4 marks]
  2. The company decides to buy the minibus which travels 100 metres in the shortest time. Determine which minibus should be bought. [4 marks]
  3. The models assume that both minibuses start moving immediately when \(t = 0\) In light of this, explain why the company may, in reality, make the wrong decision. [1 mark]
Question 15:
AnswerMarks Guidance
15(a)Integrates 0.138 (cid:1872)(cid:2870) twice AO3.4
0.046t3 c
t 0,v0c0
s 0.046t3dt
0.0115t4 k
t 0,s0k 0
0.0115t4 100
t 9.657
Finds the correct expression for
displacement condone no
AnswerMarks Guidance
consideration of cAO1.1b A1
Demonstrates at least one constant
AnswerMarks Guidance
of integration is zeroAO1.1b B1
Finds the correct time for minibus AAO1.1b A1
AnswerMarks Guidance
15(b)Integrates 0.024 (cid:1872)(cid:2871) twice AO1.1a
0.006t4 c
t 0,v0c0
s 0.006t4dt
0.0012t5 k
t 0,s0k 0
0.0012 (cid:1872)(cid:2873) (cid:3404) 100
t 9.642
9.642 < 9.657
company chooses minibus B
Finds the correct expression for
displacement condone no
AnswerMarks Guidance
consideration of cAO1.1b A1
Finds correct time for minibus BAO1.1b A1
States correct choice consistent with
‘their’ answers
Must have integrated twice in both
AnswerMarks Guidance
partsAO3.2a E1F
AnswerMarks Guidance
15(c)Explains how reaction times of each
driver could change the outcomeAO3.5b E1
than Driver A’s then A could travel
100 metres faster than B
AnswerMarks Guidance
Total9
QMarking Instructions AO 
Question 15:
--- 15(a) ---
15(a) | Integrates 0.138 (cid:1872)(cid:2870) twice | AO3.4 | M1 | v0.138t2dt
0.046t3 c
t 0,v0c0
s 0.046t3dt
0.0115t4 k
t 0,s0k 0
0.0115t4 100
t 9.657
Finds the correct expression for
displacement condone no
consideration of c | AO1.1b | A1
Demonstrates at least one constant
of integration is zero | AO1.1b | B1
Finds the correct time for minibus A | AO1.1b | A1
--- 15(b) ---
15(b) | Integrates 0.024 (cid:1872)(cid:2871) twice | AO1.1a | M1 | v0.024t3dt
0.006t4 c
t 0,v0c0
s 0.006t4dt
0.0012t5 k
t 0,s0k 0
0.0012 (cid:1872)(cid:2873) (cid:3404) 100
t 9.642
9.642 < 9.657
company chooses minibus B
Finds the correct expression for
displacement condone no
consideration of c | AO1.1b | A1
Finds correct time for minibus B | AO1.1b | A1
States correct choice consistent with
‘their’ answers
Must have integrated twice in both
parts | AO3.2a | E1F
--- 15(c) ---
15(c) | Explains how reaction times of each
driver could change the outcome | AO3.5b | E1 | If Driver B’s reaction time is greater
than Driver A’s then A could travel
100 metres faster than B
Total | 9
Q | Marking Instructions | AO | Marks | Typical Solution
A driver is road-testing two minibuses, A and B, for a taxi company.

The performance of each minibus along a straight track is compared.

A flag is dropped to indicate the start of the test.

Each minibus starts from rest.

The acceleration in m s$^{-2}$ of each minibus is modelled as a function of time, $t$ seconds, after the flag is dropped:

The acceleration of A = $0.138 t^2$
The acceleration of B = $0.024 t^3$

\begin{enumerate}[label=(\alph*)]
\item Find the time taken for A to travel 100 metres.

Give your answer to four significant figures.
[4 marks]

\item The company decides to buy the minibus which travels 100 metres in the shortest time.

Determine which minibus should be bought.
[4 marks]

\item The models assume that both minibuses start moving immediately when $t = 0$

In light of this, explain why the company may, in reality, make the wrong decision.
[1 mark]
\end{enumerate}

\hfill \mbox{\textit{AQA Paper 2 2018 Q15 [9]}}
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