The shape of the lesson
By the end of the lesson, learners can
- Acceleration is a gradient: Drag the start and end points of the line on the graph below.
- Speeding up, slowing down.
- Change in velocity first: Δv = v − u, then divide by time.
- Deceleration gives a negative acceleration.
- On a v-t graph, acceleration is the gradient of the line.
One picture every idea returns to
Acceleration is the change in velocity per unit time: a = Δv ÷ t = (v − u) ÷ t, measured in m/s². On a velocity-time graph it is the gradient of the line. A negative value means deceleration (slowing down).
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, The change in velocity, per second.. Acceleration is not about how fast you are going. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Acceleration is a gradient | Drag the start and end points of the line on the graph below. Project tab 3 of the lab (Acceleration) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Speeding up, slowing down | Speeding up, slowing down. | 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, 14 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 Speeding up, slowing down, 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 |
|---|---|
| Acceleration is Δv ÷ t, not v ÷ t. | If a car speeds up from 4 m/s to 20 m/s in 8 s, the acceleration is (20 − 4) ÷ 8 = 2.0 m/s², not 20 ÷ 8. Only when the object starts from rest (u = 0) do the two happen to agree. Always subtract the starting velocity first. |
Acceleration, deceleration and gradients: worksheet
6 questions, 14 marks. Written in the style of the papers; no past paper question is reproduced.
Define acceleration and state its SI unit.
A car speeds up from 8.0 m/s to 24 m/s in 4.0 s. Calculate its acceleration.
A cyclist slows from 20 m/s to rest in 5.0 s. Calculate the acceleration and explain what the sign of your answer means.
On a velocity-time graph, state what is represented by:
(a)the gradient of the line; (b)a line sloping downward.To find the acceleration of a car that goes from 5.0 m/s to 25 m/s in 4.0 s, a student divides 25 by 4.0. Explain the error and give the correct acceleration.
A straight section of a velocity-time graph rises from 6.0 m/s at t = 0 to 26 m/s at t = 10 s. Calculate the acceleration over this section.
Answer key and marking notes
- Acceleration is the change in velocity per unit time. ✓
- SI unit: metre per second squared (m/s²). ✓
- a = (v − u) ÷ t = (24 − 8.0) ÷ 4.0 = 16 ÷ 4.0
a = 4.0 m/s²
The negative sign shows the cyclist is decelerating (slowing down). ✓
- (a) The gradient represents the acceleration. ✓
- (b) A downward slope means the object is decelerating (negative acceleration). ✓
Acceleration uses the change in velocity, not the final velocity, so they must subtract u first. ✓
Gradient.
a = (26 − 6.0) ÷ (10 − 0) = 20 ÷ 10a = 2.0 m/s²
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 car speeds up uniformly from 8.0 m/s to 26 m/s in 6.0 s. What is its acceleration?
- A1.3 m/s²
- B3.0 m/s²
- C5.7 m/s²
- D18 m/s²
The velocity-time graph shows an object. What is its acceleration during the straight section from 2 s to 6 s?
- A0.33 m/s²
- B3.0 m/s²
- C4.0 m/s²
- D12 m/s²
A cyclist slows uniformly from 12 m/s to 3.0 m/s in 4.5 s. What is the magnitude of the deceleration?
- A0.50 m/s²
- B2.0 m/s²
- C3.3 m/s²
- D9.0 m/s²
Quiz key
a = (26 − 8.0) ÷ 6.0 = 18 ÷ 6.0 = 3.0 m/s². Option A uses the initial velocity instead of the change; C uses the sum of the velocities; D forgets to divide by the time.
gradient = (16 − 4) ÷ (6 − 2) = 12 ÷ 4 = 3.0 m/s². Option D forgets to divide by the time interval; A inverts the gradient.
(12 − 3.0) ÷ 4.5 = 9.0 ÷ 4.5 = 2.0 m/s². Option C uses the sum of the speeds; D gives the change in velocity but forgets to divide by the time.
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.