Short on time? This page is the recap. For graphs and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- Translational kinetic energy is the energy an object has because its center of mass moves.
- It is a scalar: it depends on speed, not direction. It is never negative and is zero only at rest.
- For a system of objects, add each object’s kinetic energy as a plain positive number.
- K is proportional to m and proportional to v².
- K against v is a parabola with its minimum at the origin. K against v² is a straight line through the origin with slope ½m.
- Observers in different frames can measure different kinetic energies for the same object. Both are correct in their own frame.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| K = ½mv² | m in kg, v in m/s, K in J | find kinetic energy |
| v = √(2K / m) | m/s | find speed from kinetic energy |
| 1 J = 1 kg·m²/s² | joule | check units |
| ΔK = ½mv² − ½mv₀² | J | find a change in kinetic energy |
| K_system = K₁ + K₂ + … | J | total kinetic energy of several objects |
| slope of K against v² = ½m | kg | find mass from a linearised graph |
Assumptions behind the numbers
- The object is modelled as a point at its center of mass; any spinning is ignored (rotational kinetic energy comes in Unit 6).
- All speeds are measured in one stated frame, usually the ground.
- g = 9.8 m/s² when gravity sets a speed.
Mistakes to avoid
- Forgetting to square v, or forgetting the ½.
- Doubling K when the speed doubles. It goes up by a factor of 4.
- Writing ΔK = ½m(Δv)². Subtract the two kinetic energies instead.
- Giving K a sign or a direction.
- Cancelling the kinetic energies of objects moving in opposite directions.
- Mixing frames, for example a speed relative to a ferry deck with a speed relative to the shore.
- Halving the speed when K halves. The speed falls by a factor of √2.
Quick self-check
- What is the kinetic energy of a 4.0 kg trolley at 3.0 m/s? (18 J)
- A runner triples her speed. By what factor does her kinetic energy change? (× 9)
- A 0.10 kg ball hits a wall at +5.0 m/s and rebounds at −5.0 m/s. What is ΔK? (0 J)
- A 4.0 kg object has 50 J of kinetic energy. How fast is it moving? (√(2 × 50 ÷ 4.0) = 5.0 m/s)
Next: practice questions.