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2.1.4Energy

Kinetic Energy — Oxford AQA International GCSE Combined Science - Physics Revision Notes & Topical Questions

5 min read 9 parts Lesson 5 of 12

📚 Oxford AQA International GCSE Combined Science - Physics Hub / Topical Revision
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Section 1 of 9What kinetic energy is

Kinetic energy (KE) is the energy an object has because it is moving. Anything with mass and speed has it: a rolling ball, a flowing river, a moving car. A stationary object has none. KE is a scalar and has the unit joule (J).

It is called the energy "of motion" and it is the energy that must be dissipated when something is brought to rest, for example as thermal energy in the brakes of a car.

Section 2 of 9The equation

kinetic energy = ½ × mass × speed2

Ek = ½ m v2

What the symbols mean: Ek = kinetic energy (J) · m = mass (kg) · v = speed (m s−1)

where Ek is kinetic energy in joules (J), m is mass in kilograms (kg) and v is speed in metres per second (m s−1).

The equation
The speed is squared, which is the most important feature of the formula.
Doubling the speed multiplies the KE by four; tripling the speed multiplies it by nine.
Doubling the mass only doubles the KE.

Section 3 of 9Consequences of the squared speed

Because KE depends on v2, small increases in speed require much more energy.

1
A car at 30 m s−1 (about 108 km h−1) has nine times the KE of the same car at 10 m s−1.
2
To stop it needs nine times the work done by the brakes.
3
That is why stopping distance rises so sharply with speed, and why crash energy, and so injury, climbs steeply as speed rises.

On a graph of Ek against v the curve is a parabola, starting at the origin and getting steeper. A graph of Ek against v2 is a straight line through the origin with gradient ½m. A graph of Ek against m at fixed speed is a straight line through the origin.

Section 4 of 9Working with units

Convert speeds from km h−1 into m s−1 by dividing by 3.6 (for example 72 km h−1 = 20 m s−1). Convert masses from grams to kilograms. A frequent mistake is to square only part of the expression; the order is: square the speed first, then multiply by m, then halve.

You may need to rearrangev = √(2Ek ÷ m) and m = 2Ek ÷ v2.

Section 5 of 9Linking to other ideas

Kinetic energy ties together much of this topic.

1
When a force does work on an object, the work done changes the KE.
2
When an object falls, GPE becomes KE.
3
When a vehicle brakes, KE becomes thermal energy.
4
Kinetic energy is also needed to understand collisions and why car crumple zones increase the distance over which a car is decelerated: this lowers the force on the passengers because the work done by the force (F × d) must still equal the same KE to be removed.

Section 6 of 9Everyday numbers and safety

Typical kinetic energies make the scale clear.

1
A 0.16 kg cricket ball bowled at 35 m s−1 has 0.5 × 0.16 × 1225 ≈ 98 J.
2
A cyclist and bike of total mass 80 kg moving at 8 m s−1 has 2560 J.
3
A 1000 kg car at 25 m s−1 (90 km h−1) has 312 500 J, which is more than a hundred times that of the cyclist.
4
Lorries are more dangerous both because of their larger mass and because they travel at high speed on motorways.

This is the reason for speed limits near schools: reducing the speed from 14 m s−1 (about 50 km h−1) to 9 m s−1 (about 30 km h−1) cuts the KE by about 59%, so far less energy has to be absorbed in a collision. Seat belts, air bags and crumple zones all increase the time or distance over which the kinetic energy is removed so that the force is smaller.

Section 7 of 9Worked examples

  1. Calculate the kinetic energy of a 1200 kg car travelling at 15 m s−1.

  2. The car above speeds up to 30 m s−1. By what factor does its kinetic energy change, and what is the new value?

  3. A 0.058 kg tennis ball has 29 J of kinetic energy. Find its speed.

Section 8 of 9Key terms

TermMeaning
Kinetic energyEnergy an object has due to its motion.
SpeedDistance travelled per unit time, in m s−1.
ParabolaCurve shape of Ek against v.
Stopping distanceDistance a vehicle travels while stopping; increases with v2.
Crumple zonePart of a car that deforms to lengthen the stopping distance and reduce force.

Section 9 of 9Exam technique

1
Forgetting to square the speed or squaring after multiplying by mass.
2
Forgetting the factor of ½.
3
Using km h−1 directly without converting to m s−1.
4
Thinking doubling the speed doubles the KE; it quadruples it.
5
Using grams instead of kilograms.

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