Edexcel A-level Further Maths revision notes

Work, energy and power

Section FM1-2

Year 1

1 specification point

Notes and three levels of exam-style practice for each registered specification point in this section.

Checked against Edexcel 9FM0 section FM1-2

Checked against Edexcel 9FM0 section FM1-2. Review basis: the qualification registry sourced from the Pearson Edexcel Level 3 Advanced GCE in Further Mathematics (9FM0) specification; registry verification recorded 17 July 2026.

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FM1-2.1

Kinetic and potential energy, work and power. The work-energy principle. The principle of conservation of mechanical energy.

Notes

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Explanation

Kinetic energy is $\tfrac12mv^2$ , while gravitational potential energy changes by $mg\Delta h$ . Work is force times displacement for a constant parallel force and $\int F\,dx$ when the force varies with position.
The work-energy principle states that work done by the resultant force equals the change in kinetic energy.
Mechanical energy is conserved only when no non-conservative force does work; driving forces and resistance must otherwise appear through their work.
Power is $P=dW/dt$ and equals $Fv$ only for the component of force parallel to velocity.
Examiners expect a consistent energy balance, correct signs for work and resolved forces on inclined planes.

A body moving up an incline with driving force, resistance and weight shown.

Worked example

A $900\,\text{kg}$ car travels up a slope of angle $4^\circ$ at constant speed $18\,\text{m s}^{-1}$ . Resistance is $350\,\text{N}$ . Taking $g=9.8\,\text{m s}^{-2}$ , find the engine power.

1.Constant speed gives zero resultant force along the slope.
2.The driving force is $F=900(9.8)\sin4^\circ+350=965.2\,\text{N}$ to the stated accuracy.
3. $P=Fv=965.2(18)=1.737\times10^4\,\text{W}$ .

Answer: The engine power is $17.4\,\text{kW}$ to $3$ significant figures.

Common mistakes

Don't use $mg\cos\alpha$ instead of $mg\sin\alpha$ for the component of weight down the slope.
Don't conserve mechanical energy despite a stated resistance force.
Don't use the full force magnitude in $P=Fv$ when force and velocity are not parallel.

Exam tip

State whether the equation is work-energy, conservation of energy or power before substituting values.

Tier 1 · Easy

ORIGINAL

1200\,\text{kg}

car increases its speed from

10\,\text{m s}^{-1}

14\,\text{m s}^{-1}

. Calculate the net work done on the car.

(2)

(Total for Question 1 is 2 marks)

Tier 2 · Standard

ORIGINAL

1200\,\text{kg}

car climbs a road inclined at

5^\circ

to the horizontal at a constant speed of

20\,\text{m s}^{-1}

. The resistance is

400\,\text{N}

. Taking

g=9.8\,\text{m s}^{-2}

, find the engine power.

(4)

(Total for Question 1 is 4 marks)

Tier 3 · Hard

ORIGINAL

2\,\text{kg}

particle moves along a horizontal line. A constant driving force of

20\,\text{N}

acts forwards while the resistance after displacement

x\,\text{m}

(2+0.5x)\,\text{N}

. Its speed at

x=0

3\,\text{m s}^{-1}

. Find its speed when

x=8

(5)

(Total for Question 1 is 5 marks)

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