Standard +0.8 This is a multi-step mechanics problem requiring students to: (1) use P=Fv at maximum speed to find the resistance constant k, (2) apply P=Fv again at 25 m/s to find driving force, (3) calculate net force using F=ma with resistance, and (4) find acceleration. While the individual concepts are standard A-level mechanics, the problem requires careful reasoning about when resistance equals driving force (at max speed) and coordinating multiple equations across different scenarios. The 7-mark allocation and 'fully justify' instruction indicate this is more demanding than routine textbook exercises, but it remains within reach for well-prepared Further Maths students using systematic application of standard principles.
A car of mass 1000 kg has a maximum speed of \(40\,\text{m}\,\text{s}^{-1}\) when travelling on a straight horizontal race track.
The maximum power output of the car's engine is 48 kW
The total resistance force experienced by the car can be modelled as being proportional to the car's speed.
Find the maximum possible acceleration of the car when it is travelling at \(25\,\text{m}\,\text{s}^{-1}\) on the straight horizontal race track.
Fully justify your answer.
[7 marks]
Question 5:
5 | Translates problem into equations
by modelling power as Fv and
resistance as kv | 3.3 | M1 | At 40 m s–1
Power 48000 = 40F
Resistance R = 40k
At maximum speed the driving
force equals the resistance
R = F
F = 1200 N
k = 30
Resistance = 30(25) = 750
At 25 m s–1
Power 48000 = 25D
D = 1920
Equation of motion
1920 – 750 = 1000a
a = 1.2 m s–2
Explains that at maximum speed
(or when acceleration is zero) the
driving force equals the resistance | 2.4 | E1
Obtains or uses a correct value for
k
PI by use in an expression for the
resistance | 1.1b | A1
Finds the resistance when
travelling at 25 m s–1 using ‘their’
value of k | 1.1a | M1
Finds the correct driving force
needed when travelling with
maximum power at 25 m s–1
May be embedded in an equation | 1.1a | M1
Forms a correct equation to find a | 1.1b | A1
Finds the correct value of a stating
correct units
AWRT 1.2 | 3.2a | A1
Total | 7
Q | Marking Instructions | AO | Marks | Typical Solution
A car of mass 1000 kg has a maximum speed of $40\,\text{m}\,\text{s}^{-1}$ when travelling on a straight horizontal race track.
The maximum power output of the car's engine is 48 kW
The total resistance force experienced by the car can be modelled as being proportional to the car's speed.
Find the maximum possible acceleration of the car when it is travelling at $25\,\text{m}\,\text{s}^{-1}$ on the straight horizontal race track.
Fully justify your answer.
[7 marks]
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2019 Q5 [7]}}