Kinetic energy · Grade 12
In Grade 12 you get fluent with: kinetic energy = ½mv²; how mass and speed change kinetic energy; finding speed or mass from kinetic energy.
Anything that moves has energy in its kinetic store. The kinetic energy depends on the mass and, even more, on the speed: KE = ½mv². Doubling the mass doubles the kinetic energy, but doubling the speed makes it four times bigger. That is why a small rise in a car’s speed needs a much longer distance to stop.
Key facts
- Kinetic energy KE = ½mv².
- Doubling speed makes KE four times bigger; doubling mass doubles it.
- To find a speed from kinetic energy, rearrange: v = √(2KE ÷ m).
Worked examples
Example 1
A 0.5 kg ball moves at 4 m/s. Find its kinetic energy.
Answer: 4 J
Example 2
A 60 kg runner moves at 5.0 m/s. Find her kinetic energy.
Answer: 750 J
Example 3
A 1,200 kg car travels at 15 m/s. Find its kinetic energy.
Answer: 135,000 J (135 kJ)
Example 4
A 1,000 kg car travels at 20 m/s. What is its kinetic energy in kJ?
Answer: 200 kJ
Example 5
Two trolleys roll along. One has 3 times the mass of the other (everything else the same). How does its kinetic energy compare?
Answer: 3 times as much
Example 6
Two trolleys roll along. One has 4 times the speed of the other (everything else the same). How does its kinetic energy compare?
Answer: 16 times as much
Example 7
A car speeds up from 60 km/h to 80 km/h. By what factor does its kinetic energy increase? Give your answer to 2 decimal places.
Answer: 1.78
Example 8
An object moving at 18 m/s has 1,053 J of kinetic energy. What is its mass?
Answer: 6.5 kg
Example 9
A 0.058 kg tennis ball has 8.38 J of kinetic energy. How fast is it moving? Give your answer to 1 decimal place.
Answer: 17.0 m/s