AQA AS Paper 1 2022 June — Question 16 6 marks

Exam BoardAQA
ModuleAS Paper 1 (AS Paper 1)
Year2022
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConstant acceleration (SUVAT)
TypeDisplacement expressions and comparison
DifficultyModerate -0.3 This is a straightforward kinematics problem requiring application of SUVAT equations. Part (a) involves setting up relative motion equations and algebraic manipulation to reach the given result (4 marks for a 'show that' is generous). Part (b) requires finding t from v=u+at, then substituting into the formula. The problem is slightly easier than average as it's highly structured, uses standard techniques, and the 'show that' format guides students to the answer.
Spec3.02d Constant acceleration: SUVAT formulae
Jermaine and his friend Meena are walking in the same direction along a straight path. Meena is walking at a constant speed of \(u\) m s\(^{-1}\) Jermaine is walking 0.2 m s\(^{-1}\) more slowly than Meena. When Jermaine is \(d\) metres behind Meena he starts to run with a constant acceleration of 2 m s\(^{-2}\), for a time of \(t\) seconds, until he reaches her.
  1. Show that $$d = t^2 - 0.2t$$ [4 marks]
  2. When Jermaine's speed is 7.8 m s\(^{-1}\), he reaches Meena. Given that \(u = 1.4\) find the value of \(d\). [2 marks]
Question 16:
AnswerMarks
16(a)Uses appropriate constant
acceleration equation to find
expression for displacement of
Jermaine seconds after
acceleration begins, with at least
AnswerMarks Guidance
one term c𝑑𝑑orrect.3.1b M1
2
𝑠𝑠 = (π‘’π‘’βˆ’0.2)𝑑𝑑+0.5Γ—2𝑑𝑑
Reaches Meena when
𝑠𝑠 = 𝑒𝑒𝑑𝑑+𝑑𝑑
2
𝑒𝑒𝑑𝑑+𝑑𝑑 = (π‘’π‘’βˆ’0.2)𝑑𝑑+𝑑𝑑
2
𝑒𝑒𝑑𝑑+𝑑𝑑 = π‘’π‘’π‘‘π‘‘βˆ’0.2𝑑𝑑 +𝑑𝑑
2
𝑑𝑑 = 𝑑𝑑 βˆ’0.2𝑑𝑑
Obtains fully correct equation for
Jermaine’s displacement PI
Or 2
𝑠𝑠 = (π‘’π‘’βˆ’0.2)𝑑𝑑+0.5Γ—2𝑑𝑑
AnswerMarks Guidance
21.1b A1
𝑠𝑠 = (π‘’π‘’βˆ’0.2)𝑑𝑑+0.5Γ—2𝑑𝑑 βˆ’π‘‘π‘‘
Forms a correct expression for
Meena’s displacement.
or
AnswerMarks Guidance
𝑠𝑠D o= n𝑒𝑒o𝑑𝑑t acc𝑠𝑠e p=t 𝑒𝑒ut𝑑𝑑 –+ d𝑑𝑑3.1b B1
Completes reasoned argument
to obtain given result.
AnswerMarks Guidance
AG2.1 R1
Subtotal4
QMarking instructions AO
AnswerMarks
16(b)Uses appropriate constant
acceleration equation to find
AnswerMarks Guidance
value for3.1b M1
𝑑𝑑 =3.3 ⇒𝑑𝑑 = 10.23
𝑑𝑑
Uses given equation to find
correct value of d
AnswerMarks Guidance
Accept 10.2 or 10.231.1b A1
Subtotal2
Question 16 Total6
QMarking instructions AO 
Question 16:
--- 16(a) ---
16(a) | Uses appropriate constant
acceleration equation to find
expression for displacement of
Jermaine seconds after
acceleration begins, with at least
one term c𝑑𝑑orrect. | 3.1b | M1 | Jermaine’s displacement
2
𝑠𝑠 = (π‘’π‘’βˆ’0.2)𝑑𝑑+0.5Γ—2𝑑𝑑
Reaches Meena when
𝑠𝑠 = 𝑒𝑒𝑑𝑑+𝑑𝑑
2
𝑒𝑒𝑑𝑑+𝑑𝑑 = (π‘’π‘’βˆ’0.2)𝑑𝑑+𝑑𝑑
2
𝑒𝑒𝑑𝑑+𝑑𝑑 = π‘’π‘’π‘‘π‘‘βˆ’0.2𝑑𝑑 +𝑑𝑑
2
𝑑𝑑 = 𝑑𝑑 βˆ’0.2𝑑𝑑
Obtains fully correct equation for
Jermaine’s displacement PI
Or 2
𝑠𝑠 = (π‘’π‘’βˆ’0.2)𝑑𝑑+0.5Γ—2𝑑𝑑
2 | 1.1b | A1
𝑠𝑠 = (π‘’π‘’βˆ’0.2)𝑑𝑑+0.5Γ—2𝑑𝑑 βˆ’π‘‘π‘‘
Forms a correct expression for
Meena’s displacement.
or
𝑠𝑠D o= n𝑒𝑒o𝑑𝑑t acc𝑠𝑠e p=t 𝑒𝑒ut𝑑𝑑 –+ d𝑑𝑑 | 3.1b | B1
Completes reasoned argument
to obtain given result.
AG | 2.1 | R1
Subtotal | 4
Q | Marking instructions | AO | Marks | Typical solution
--- 16(b) ---
16(b) | Uses appropriate constant
acceleration equation to find
value for | 3.1b | M1 | 7.8= (1.4βˆ’0.2)+2𝑑𝑑
𝑑𝑑 =3.3 ⇒𝑑𝑑 = 10.23
𝑑𝑑
Uses given equation to find
correct value of d
Accept 10.2 or 10.23 | 1.1b | A1
Subtotal | 2
Question 16 Total | 6
Q | Marking instructions | AO | Marks | Typical solution
Jermaine and his friend Meena are walking in the same direction along a straight path.

Meena is walking at a constant speed of $u$ m s$^{-1}$

Jermaine is walking 0.2 m s$^{-1}$ more slowly than Meena.

When Jermaine is $d$ metres behind Meena he starts to run with a constant acceleration of 2 m s$^{-2}$, for a time of $t$ seconds, until he reaches her.

\begin{enumerate}[label=(\alph*)]
\item Show that
$$d = t^2 - 0.2t$$
[4 marks]

\item When Jermaine's speed is 7.8 m s$^{-1}$, he reaches Meena.

Given that $u = 1.4$ find the value of $d$.
[2 marks]
\end{enumerate}

\hfill \mbox{\textit{AQA AS Paper 1 2022 Q16 [6]}}
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