The shape of the lesson
By the end of the lesson, learners can
- Push the speed, watch energy leap: Change the mass and the speed and read the kinetic energy.
- Why the square matters: The defining equation, and the form rearranged for speed:
- Square the speed before multiplying by half the mass.
- Double speed: four times the kinetic energy.
- Rearranging: v = √(2KE ÷ m).
One picture every idea returns to
Kinetic energy is the energy of a moving object: KE = ½mv², measured in joules. The velocity is squared, so doubling the speed multiplies the kinetic energy by four, not two.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Speed counts twice.. A car at 60 km/h does not carry twice the energy of one at 30 km/h, it carries four times as much. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Push the speed, watch energy leap | Change the mass and the speed and read the kinetic energy. Project tab 3 of the lab (Kinetic energy) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Why the square matters | The defining equation, and the form rearranged for speed: Model the worked example Worked example on the board, one line at a time. | Numbered Heads Together |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 13 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Why the square matters, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Numbered Heads Together
Teams of four number off. Put up a question, give the team time to make sure every member can answer, then call a number: that student answers for the team, so nobody can leave the thinking to someone else.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Square the speed before multiplying, and do it first. | A common slip is to work out ½mv and forget the square, or to square the whole expression. Only the speed is squared. Because of that square, doubling the speed multiplies the kinetic energy by four, and tripling it multiplies the energy by nine. |
Kinetic energy (KE = ½mv²): worksheet
6 questions, 13 marks. Written in the style of the papers; no past paper question is reproduced.
Write the equation for kinetic energy and state its unit.
Calculate the kinetic energy of a 1200 kg car moving at 15 m/s.
A 2.0 kg ball moves at 6.0 m/s. Calculate its kinetic energy.
A car doubles its speed. State the factor by which its kinetic energy increases, and explain why.
A 4.0 kg object has a kinetic energy of 200 J. Calculate its speed.
Explain, using kinetic energy, why even a modest increase in a car's speed greatly increases the damage in a crash.
Answer key and marking notes
- KE = ½mv². ✓
- Unit: joule (J). ✓
- KE = ½ × 1200 × 15² = ½ × 1200 × 225
135000 J (135 kJ)
- KE = ½ × 2.0 × 6.0² = ½ × 2.0 × 36
36 J
- The kinetic energy increases by a factor of four. ✓
- KE depends on the square of the speed, and 2² = 4. ✓
- 200 = ½ × 4.0 × v²
v² = 200 ÷ 2.0 = 100
v = √100
v = 10 m/s
- 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. ✓
3 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
A 2.0 kg object moves at 5.0 m/s. What is its kinetic energy?
- A5.0 J
- B10 J
- C25 J
- D50 J
The speed of a moving car doubles. By what factor does its kinetic energy change?
- Ait stays the same
- Bit doubles
- Cit becomes 4 times larger
- Dit becomes 8 times larger
A 0.40 kg ball has 12.8 J of kinetic energy. What is its speed?
- A5.7 m/s
- B8.0 m/s
- C32 m/s
- D64 m/s
Quiz key
KE = ½mv² = ½ × 2.0 × 5.0² = ½ × 2.0 × 25 = 25 J. Option D (50 J) forgets the factor of ½; B uses ½mv without squaring the speed.
Because KE ∝ v², doubling the speed multiplies the kinetic energy by 2² = 4. Option B assumes a direct (linear) relationship, the most common error here.
12.8 = ½ × 0.40 × v², so v² = 64 and v = 8.0 m/s. Option D stops at v² = 64 without taking the square root.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.