Standard +0.8 This question requires students to interpret a velocity-time graph, understand that displacement equals area under the curve (with sign), set up an equation involving areas of trapezoids/triangles with an unknown time value, and solve algebraically. It goes beyond routine graph reading by requiring problem-solving with the constraint that total displacement equals -7m, making it moderately challenging but still within standard A-level scope.
15 A car is moving in a straight line along a horizontal road.
The graph below shows how the car's velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) changes with time, \(t\) seconds.
\includegraphics[max width=\textwidth, alt={}, center]{ad6590e8-6673-45ca-bef3-a14716978827-23_509_746_456_648}
Over the period \(0 \leq t \leq 15\) the car has a total displacement of - 7 metres.
Initially the car has velocity \(0 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
Find the next time when the velocity of the car is \(0 \mathrm {~ms} ^ { - 1 }\)
[0pt]
[4 marks]
Correct expression for area of triangle above time axis in terms of variable for time
Area below \(= 2(10-t) + 20\)
B1 (1.1b)
Correct expression for area of triangle or trapezium below time axis; accept negative area for displacement
\(2t + 7 = 2(10-t) + 20\)
M1 (3.1b)
Forms equation with single variable using expressions for area; area above \(-\) area below \(= \pm k\) where \(k\) is one of 3, 7, 13 or 17
\(t = 8.25\) seconds
A1 (1.1b)
Condone missing or incorrect units
## Question 15:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Area above $= 2t$ | B1 (1.1b) | Correct expression for area of triangle above time axis in terms of variable for time |
| Area below $= 2(10-t) + 20$ | B1 (1.1b) | Correct expression for area of triangle or trapezium below time axis; accept negative area for displacement |
| $2t + 7 = 2(10-t) + 20$ | M1 (3.1b) | Forms equation with single variable using expressions for area; area above $-$ area below $= \pm k$ where $k$ is one of 3, 7, 13 or 17 |
| $t = 8.25$ seconds | A1 (1.1b) | Condone missing or incorrect units |
15 A car is moving in a straight line along a horizontal road.
The graph below shows how the car's velocity $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ changes with time, $t$ seconds.\\
\includegraphics[max width=\textwidth, alt={}, center]{ad6590e8-6673-45ca-bef3-a14716978827-23_509_746_456_648}
Over the period $0 \leq t \leq 15$ the car has a total displacement of - 7 metres.\\
Initially the car has velocity $0 \mathrm {~m} \mathrm {~s} ^ { - 1 }$\\
Find the next time when the velocity of the car is $0 \mathrm {~ms} ^ { - 1 }$\\[0pt]
[4 marks]\\
\hfill \mbox{\textit{AQA Paper 2 2022 Q15 [4]}}