Extended · Practice questions · Kinetic energy

Half m v squared.

Six original Cambridge-style questions on calculating kinetic energy, rearranging for speed or mass, and the squared-speed relationship.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Square first

KE = ½mv².

Square the speed before multiplying by half the mass.
Double speed: four times the kinetic energy.
Rearranging: v = √(2KE ÷ m).

[2 marks]

Write the equation for kinetic energy and state its unit.

KE = ½mv². ✓
Unit: joule (J). ✓

Calculation

[2 marks]

Calculate the kinetic energy of a 1200 kg car moving at 15 m/s.

KE = ½ × 1200 × 15² = ½ × 1200 × 225

135000 J (135 kJ)

Calculation

[2 marks]

A 2.0 kg ball moves at 6.0 m/s. Calculate its kinetic energy.

KE = ½ × 2.0 × 6.0² = ½ × 2.0 × 36

36 J

Analysis

[2 marks]

A car doubles its speed. State the factor by which its kinetic energy increases, and explain why.

The kinetic energy increases by a factor of four. ✓
KE depends on the square of the speed, and 2² = 4. ✓

Calculation

[3 marks]

A 4.0 kg object has a kinetic energy of 200 J. Calculate its speed.

200 = ½ × 4.0 × v² v² = 200 ÷ 2.0 = 100 v = √100

v = 10 m/s

Analysis

[2 marks]

Explain, using kinetic energy, why even a modest increase in a car's speed greatly increases the damage in a crash.

Kinetic energy is proportional to the square of the speed. ✓
So a small rise in speed causes a much larger rise in kinetic energy, which must all be transferred in the crash, causing more damage. ✓