Kinetic energy, ke
3 marks · NormalExplain, using the relationship for kinetic energy, why a small increase in speed leads to a much larger increase in kinetic energy.
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Because kinetic energy depends on the square of speed, so doubling the speed will increase kinetic energy by four times. Even a small increase in speed increases the value of v squared significantly, leading to a much higher kinetic energy.
Must show: mention of square/squared, states that increase is more than proportional, quantitative example or reasoning
Common mistakes: Claiming KE just doubles if speed doubles
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Marking points
B1 · 1 mark · Mentions dependence on v squared/square of speed
B2 · 1 mark · Explains that a small increase in v results in larger increase in KE
B3 · 1 mark · Quantitative example or reasoning (e.g. doubling v quadruples KE)
Worked solution
Kinetic energy is given by KE = 1/2 m v^2. Since KE depends on speed squared, a small change in v has a large effect on KE. For example, if speed increases from 2 m/s to 4 m/s, KE becomes four times greater. So if speed doubles, kinetic energy increases by a factor of four.