AQA Further Paper 3 Mechanics Specimen — Question 7 5 marks

Exam BoardAQA
ModuleFurther Paper 3 Mechanics (Further Paper 3 Mechanics)
SessionSpecimen
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPower and driving force
TypeMaximum speed on incline vs horizontal
DifficultyStandard +0.3 This is a straightforward application of the power-force-velocity relationship (P = Fv) combined with resolving forces on an incline. Students must equate driving force to resistance plus component of weight down the slope, then solve for v. While it involves multiple steps, each is standard and the question clearly signposts the method with no novel insight required.
Spec3.03v Motion on rough surface: including inclined planes6.02l Power and velocity: P = Fv

7 In this question use \(g = 9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
When a car, of mass 1200 kg , travels at a speed of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) it experiences a total resistive force which can be modelled as being of magnitude \(36 v\) newtons.
The maximum power of the car is 90 kilowatts.
The car starts to descend a hill, inclined at \(5.2 ^ { \circ }\) to the horizontal, along a straight road.
Find the maximum speed of the car down this hill.
[0pt] [5 marks]

Question 7:
AnswerMarks Guidance
Driving force \(= \dfrac{90000}{v}\)B1 Uses \(P = Fv\)
\(\dfrac{90000}{v} + 1200g\sin(5.2°) - 36v = 0\)M1 Forms equation with resultant force \(= 0\); condone sign errors
\(36v^2 - 1200g\sin(5.2°)v - 90000 = 0\)A1 Fully correct equation
Rearranges to quadratic formM1 PI by correct answer
\(v = 67\text{ m s}^{-1}\)A1F Correct speed to 2 sf; FT if both M1 marks awarded
## Question 7:
| Driving force $= \dfrac{90000}{v}$ | B1 | Uses $P = Fv$ |
| $\dfrac{90000}{v} + 1200g\sin(5.2°) - 36v = 0$ | M1 | Forms equation with resultant force $= 0$; condone sign errors |
| $36v^2 - 1200g\sin(5.2°)v - 90000 = 0$ | A1 | Fully correct equation |
| Rearranges to quadratic form | M1 | PI by correct answer |
| $v = 67\text{ m s}^{-1}$ | A1F | Correct speed to 2 sf; FT if both M1 marks awarded |

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7 In this question use $g = 9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.\\
When a car, of mass 1200 kg , travels at a speed of $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ it experiences a total resistive force which can be modelled as being of magnitude $36 v$ newtons.\\
The maximum power of the car is 90 kilowatts.\\
The car starts to descend a hill, inclined at $5.2 ^ { \circ }$ to the horizontal, along a straight road.\\
Find the maximum speed of the car down this hill.\\[0pt]
[5 marks]\\

\hfill \mbox{\textit{AQA Further Paper 3 Mechanics  Q7 [5]}}