GCSE · Physics · Edexcel · Spec 1PH0

Acceleration equation

A car cruising at a steady 30 m/s isn't accelerating. One pulling away from the lights is. Acceleration isn't how fast you're going — it's how fast your velocity changes.

Predict, then check

Watch the velocity climb

A cyclist is moving at 4 m/s when the clock starts. Four seconds later they're moving at 16 m/s, and they speed up by the same amount every single second. Drag each second's velocity to where you think it sits on the line (in m/s).

0 s — Velocity at 0 s1 s — Velocity at 1 s2 s — Velocity at 2 s3 s — Velocity at 3 s4 s — Velocity at 4 s

Calculating acceleration

Problem

A train speeds up steadily from 12 m/s to 30 m/s in 9 s. Calculate its acceleration.

Which idea do you hold?

A car brakes

A car is moving at 20 m/s. The driver brakes steadily, and 4 s later the car is moving at 8 m/s.

What is the car's acceleration? Pick the answer closest to what you'd write.

−3 m/s². The velocity changed by 8 − 20 = −12 m/s in 4 s, and −12 ÷ 4 = −3.3 m/s². I got −3, but an acceleration can't be negative, so the minus sign must be a mistake.2 m/s². The car ends at 8 m/s, and 8 ÷ 4 = 2.5 m/s². It was going fast — 20 m/s — and 20 ÷ 4 = 5, so it has a big acceleration.

How sure are you?

I'm sureI think soI'm guessing

−3 m/s². The velocity changed by 8 − 20 = −12 m/s in 4 s, and −12 ÷ 4 = −3.

This matches the evidence

Spot on. Here u = 20 m/s and v = 8 m/s, so v − u = −12 m/s. Shared over 4 s, that's −3 m/s². The minus sign isn't a slip — it tells you the velocity is going down by 3 m/s every second. The car is still moving forwards, so here that means it's slowing down.

3 m/s². I got −3, but an acceleration can't be negative, so the minus sign must be a mistake.

This is a common misconception

Your working was right — it's the last step that loses the meaning. A negative acceleration is a perfectly good answer: it means the velocity is decreasing. Drop the sign and you've described a car speeding up by 3 m/s every second, which is the opposite of braking.

2 m/s². The car ends at 8 m/s, and 8 ÷ 4 = 2.

This is a common misconception

That divides the final velocity on its own. Acceleration is about the CHANGE in velocity, v − u. The car didn't go from 0 to 8 m/s; it went from 20 m/s down to 8 m/s. Subtract u first, then divide.

5 m/s². It was going fast — 20 m/s — and 20 ÷ 4 = 5, so it has a big acceleration.

This is a common misconception

How fast something is going is its velocity, not its acceleration. A car cruising at a steady 20 m/s has an acceleration of zero, because its velocity isn't changing. Acceleration only cares how much the velocity changes each second.

Subtract first (v − u), keep the sign, then divide by t. A minus answer means the velocity is decreasing.

Your turn

Finding the time

A bus joining a main road speeds up steadily from 4 m/s to 13 m/s. Its acceleration is 1.5 m/s². How long does this take?

Start from a = (v − u) / t. This time we know a and want t.Known: u = 4 m/s, v = 13 m/s, a = 1.5 m/s².
missing step

Which line is step 2?

Rearrange for t: t = a × (v − u)Rearrange for t: t = (v − u) / aRearrange for t: t = a / (v − u)

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

How much does the velocity change every second?

What you need to know

Acceleration is the change in velocity per second: acceleration = change in velocity ÷ time taken.
In symbols, a = (v − u) / t: u is the starting velocity, v is the final velocity, and v − u is the change in velocity.
Units: acceleration in metres per second squared (m/s²), velocity and change in velocity in metres per second (m/s), time in seconds (s).
The equation rearranges to t = (v − u) / a and v − u = a × t.

The big picture

Acceleration is how much an object's velocity changes every second. You find it by taking the change in velocity (final velocity minus starting velocity) and dividing by the time taken: a = (v − u) / t. Acceleration is measured in m/s² — metres per second, every second. A negative answer means the velocity is decreasing.

Key points

1Acceleration measures how quickly velocity changes, not how fast something is moving.

2Subtract before you divide: find v − u first, then divide by t.

3m/s² means 'm/s gained (or lost) every second'.

4A negative acceleration means the velocity is decreasing.

5An object moving at a steady velocity has zero acceleration.

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Worked example

Problem

A ball rolls down a slope. It starts at 2 m/s and accelerates steadily at 0.5 m/s² for 8 s. What is its final velocity?

⚠ Watch out

Dividing the final velocity by the time (v ÷ t) and forgetting to subtract the starting velocity u. That only gives the right answer when the object starts from rest, where u = 0.

🧠

Memory hook

Change, then share: find the change in velocity (v − u), then share it out over the seconds (÷ t).

✓

Check yourself

A skateboarder speeds up steadily from 3 m/s to 11 m/s in 4 s. What is their acceleration? (Answer: (11 − 3) ÷ 4 = 2 m/s².)

Flashcards

(10)

What does acceleration measure?

How much an object's velocity changes each second.

Acceleration word equation

acceleration = change in velocity ÷ time taken

Acceleration symbol equation

a = (v − u) / t

In a = (v − u) / t, what are u and v?

u is the initial (starting) velocity; v is the final velocity.

Unit of acceleration — and what it means

m/s², metres per second squared: the m/s gained or lost every second.

Which quantities in a = (v − u) / t are measured in m/s?

v, u and v − u — they are all velocities.

What does a negative acceleration tell you?

The velocity is decreasing.

Rearrange a = (v − u) / t to find t

t = (v − u) / a

Rearrange a = (v − u) / t to find the change in velocity

v − u = a × t

Acceleration of a lorry moving at a steady 25 m/s?

0 m/s² — its velocity isn't changing.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Acceleration equation

Watch the velocity climb

Build the symbol grid

A car brakes

Finding the time

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