Acceleration is the rate of change of velocity, a = Δv ÷ Δt, in m/s². It has a direction, the same as the net force. Slowing down is acceleration too (opposite to the motion), and on a speed–time graph acceleration is the gradient.
A Formula 1 car reaches 100 km/h in under 3 seconds. A train takes about 40. Both end up fast; one accelerates far more. Fast and accelerating are not the same thing.
In everyday talk "accelerate" means speed up. In physics it means something more exact.
Engage: Commit to a prediction before you test anything. A wrong guess is fine: it shows you what to look for.
Explore: Try it on the board and compare what happens with your prediction.
Explain: Use the particle model to explain what you saw.
Elaborate: Use the same idea in a new context.
Evaluate: Look back at your first ideas and what changed.
WidthMore contexts, same idea.
Make your prediction first. Help opens once you've locked it in.
EngageCommit to a prediction before you test anything. A wrong guess is fine: it shows you what to look for.
Engage: fast or accelerating?
ExploreTry it on the board and compare what happens with your prediction.
Explore: read the graph
Press Play. Watch how much the speed goes up each second (the graph and the numbers under it).
Try it yourselfYour edits are saved in this browser.
Run the trolley with a 6 N push for at least 4 seconds.
Use the board. This ticks when you get there.
ExplainUse the particle model to explain what you saw.
Explain: a = Δv ÷ Δt
In your book: explain why a car cruising at 100 km/h has zero acceleration, and a car pulling away from traffic lights has some.
The trolley went from 0 to 12 m/s in 4 s. What was its acceleration, in m/s²?
A cyclist goes from 2 m/s to 10 m/s in 4 s. Acceleration, in m/s²?
Is it accelerating?
A car cruising at a steady 100 km/h on a straight roadFast, but its velocity isn't changing.
A bike slowing down for traffic lightsSlowing down is acceleration, opposite to the motion.
A runner rounding a bend at a steady speedIts direction changes, so its velocity changes.
A trolley speeding up from rest
A parked car
Elaborate TypicalUse the same idea in a new context.
Elaborate: slowing down
Try it yourselfYour edits are saved in this browser.
Let the moving trolley slow to a stop.
Use the board. This ticks when you get there.
It went from 8 m/s to 0 in 4 s. What was its acceleration, in m/s²? (Use a minus sign for slowing down.)
Elaborate WiderUse the same idea in a new context.
Elaborate: turning
EvaluateLook back at your first ideas and what changed.
Evaluate: look back
Write one sentence: "At first I thought… Now I think… because…"
Revision summary
Acceleration is the rate of change of velocity: a = Δv ÷ Δt, in m/s².
It has a direction, the same as the net force. Slowing down is acceleration opposite to the motion (negative).
A fast object at a steady speed has zero acceleration.
On a speed–time graph, acceleration is the gradient.
For teachers
Students define acceleration as the rate of change of velocity, calculate it from data and graphs in m/s², and treat it as a vector in the direction of the net force (AC9S10U05, node 3, a hinge node). About 25 minutes.
I can define acceleration as the rate of change of velocity, in m/s².
I can calculate acceleration from velocity and time data, and read it from a speed–time graph.
I can explain that acceleration has a direction, the same as the net force; slowing down is acceleration too.
Before class
A concept tutorial for introducing or revising the idea; it does not replace motion sensors or ticker timers. Set the width with ?width=minimum, typical (default) or wider.
The hinge is the shift from the everyday word to a defined quantity. Keep separating "fast" from "changing speed".
Board notes: the board's acceleration reading appears under the board, so the number checks use different numbers from the board where possible. The slowing-down board uses friction 4 N on 2 kg: a = −2 m/s².
Running the lesson
Engage: ask why the cruising car isn't accelerating. Most will say it is.
Explore: pause at 1, 2 and 3 seconds and read the speed: +3 m/s each time.
Explain: insist on units for every answer aloud.
In your own words: the cruising-car explanation is the evidence.
The hard part (on purpose)
Separating acceleration (change in velocity) from speed. When a student says a fast car has a big acceleration, ask whether its speed is changing.
When students get stuck
A student says a fast car has big acceleration. Ask: Is its speed changing? Fix: No, so its acceleration is zero. Acceleration is the change, not the speed.
A student gives acceleration in m/s. Ask: How much speed is added, and in how long? Fix: m/s added per second: m/s².
A student says slowing down isn't acceleration. Ask: Is the velocity changing? Fix: Yes, so it's accelerating, backwards (negative).
Stretch and support
Stretch: A ball thrown straight up slows down, stops for an instant, then falls. What is its acceleration at the very top?
Support: Give the formula card: a = (final speed − starting speed) ÷ time, with one worked example.
Where it leads
Next: F = ma (node 4), which links the acceleration to the net force and the mass.
In class: a motion sensor and a trolley on a ramp, or a ticker timer.
What each step is for
Engage: fast or accelerating?: Students who equate acceleration with speed will choose the fast cruising car; the graph shows acceleration as change, not speed.
Explore: read the graph: Watching a straight-line speed–time graph build up, with the acceleration read out, links the gradient to a rate before the formula appears.
Explain: a = Δv ÷ Δt: Calculating acceleration from data, then giving it a direction, turns the everyday word into a defined vector quantity.
Elaborate: slowing down: A negative acceleration (opposite to the motion) shows acceleration as a direction, not just 'more speed'.
Elaborate: turning: A constant-speed turn is acceleration with no change of speed, the hardest case for 'acceleration = speeding up'.
Now you can
Define acceleration as the rate of change of velocity, in m/s².
Calculate acceleration from velocity and time data, and read it from a speed–time graph.
Explain that acceleration has a direction, the same as the net force; slowing down is acceleration too.