Acceleration in physics is the rate at which an object’s velocity changes with time. It is calculated as a = Δv/Δt — the change in velocity divided by the time taken — and measured in metres per second squared (m/s²). Because velocity includes direction, speeding up, slowing down and turning all count as acceleration.
Feel that push into your seat as a plane begins its take-off run? That is acceleration making itself felt — your velocity is climbing by several metres per second, every second, and your body registers every one of them.
A speedometer tells you how fast you are going. Acceleration tells you how quickly “how fast” is changing — and once that one idea clicks, half of mechanics falls into place.
What Is Acceleration in Physics?
Hold the idea this way: speed describes how quickly your position changes; acceleration describes how quickly your velocity changes. A cruising airliner doing 900 km/h in a straight line has zero acceleration. A sprinter exploding off the blocks — moving far slower — has plenty.
Formally, acceleration is the rate of change of velocity with time. It is a vector: it has a size and a direction, and both matter.
Average vs instantaneous acceleration
Average acceleration takes the total change in velocity and divides it by the total time — ideal for whole journeys. Instantaneous acceleration is the value at one exact moment, found by shrinking that time interval until it is vanishingly small.
If you go on to calculus, you will meet the instantaneous version as a = dv/dt, the derivative of velocity with respect to time. In a first physics course, the average form does almost all of the work.
The Acceleration Formula (and What m/s² Means)
Everything starts from one definition. Memorise this and you can rebuild the rest.
| Symbol | Meaning | SI unit |
|---|---|---|
| a | acceleration | metres per second squared (m/s²) |
| Δv | change in velocity (v − u) | metres per second (m/s) |
| u | initial velocity | m/s |
| v | final velocity | m/s |
| t (Δt) | time taken for the change | seconds (s) |
| s | displacement (used below) | metres (m) |
So what does m/s² actually mean? Read it as “(metres per second) per second”: an acceleration of 3 m/s² adds 3 m/s of velocity during every second that passes. One second in, you have gained 3 m/s; two seconds in, 6 m/s.
The constant-acceleration toolkit
Rearrange the definition and you get the most-used equation in kinematics — final velocity from initial velocity, acceleration and time:
And when you know the distance but not the time, this companion equation — valid only while acceleration is constant — closes the gap:
- s is the displacement in metres (m); all other symbols are exactly as in the table above.
- Both equations assume uniform acceleration — a straight line on a velocity–time graph.
Reading acceleration from a velocity–time graph
Plot velocity against time and acceleration stops being abstract: it is simply the slope of the line. A straight line means constant acceleration; a horizontal line means none at all.
On a velocity–time graph, acceleration is the slope: this line climbs 6 m/s every 2 s, so a = 3 m/s².
This is the car from Worked Problem 1 below: 0 to 24 m/s in 8 seconds. Pick any triangle on the line and rise over run gives the same answer — 3 m/s².
How Acceleration Works: Speed, Direction and Vectors
Velocity is a vector — a speed plus a direction. Change either ingredient and you have accelerated. That single fact unifies three situations students often treat as separate.
Speeding up and slowing down
When acceleration points the same way as velocity, the object speeds up. When it points the opposite way — brakes, or friction dragging on a sliding box — it slows down. Everyday language calls the slowing case deceleration, but to a physicist it is simply acceleration with a negative sign along the chosen direction.
Changing direction counts too
Here is the one that catches nearly everyone: an object turning at constant speed is still accelerating, because its direction — and therefore its velocity — is changing. For motion in a circle, the acceleration points toward the centre and has size:
- a — centripetal acceleration, directed toward the centre of the circle (m/s²)
- v — speed along the circular path (m/s)
- r — radius of the circle (m)
That centre-pointing pull is the sideways press you feel on a roundabout. The speedometer never moves — yet you accelerate the whole way round.
Three faces of one quantity: acceleration is any change in velocity — magnitude, direction, or both.
Sliders beat sentences here. Set an initial velocity and an acceleration below, press run, and watch the velocity–time line draw itself — the slope is exactly the acceleration you chose.
Acceleration vs Velocity: What’s the Difference?
Velocity is where your motion stands right now; acceleration is where it is heading. Confusing the two is the single most common error in introductory mechanics, so it pays to nail the distinction once and for all.
If speed vs velocity is still fuzzy, start with our guide to velocity vs speed — this comparison builds directly on it.
| Velocity | Acceleration | |
|---|---|---|
| Definition | rate of change of position | rate of change of velocity |
| Formula | displacement ÷ time | change in velocity ÷ time |
| SI unit | m/s | m/s² |
| Vector? | yes — magnitude and direction | yes — magnitude and direction |
| Zero when… | the object is (momentarily) at rest | velocity is constant — steady speed in a straight line |
| On the road | the speedometer reading, plus your heading | the push you feel — throttle, brakes, corners |
One classic trap: a ball thrown straight up has zero velocity at the very top of its flight — yet its acceleration there is still 9.81 m/s² downward. Velocity can pass through zero while acceleration carries on regardless.
Acceleration Due to Gravity
Drop anything near Earth’s surface and — air resistance aside — it gains speed at the same steady rate: about 9.81 m/s², a value so important it earns its own symbol, g. One second into free fall you are moving at roughly 9.8 m/s; two seconds in, 19.6 m/s.
g is not perfectly uniform. It runs from about 9.78 m/s² at the equator to about 9.83 m/s² at the poles, which is why exam papers happily round it to 9.8 — or even 10 — m/s².
Mass makes no difference: a hammer and a feather fall together in vacuum, as the Apollo 15 crew famously demonstrated on the Moon, where g is only about 1.6 m/s². And once gravity pulls a ball sideways as well as down, you are into projectile motion.
Real-World Examples of Acceleration
Numbers turn a definition into intuition. Here are five accelerations you have personally felt, with realistic magnitudes.
- Pulling away from the lights: a family car reaching 100 km/h (27.8 m/s) in about 9 s averages roughly 3 m/s² — brisk but comfortable.
- An emergency stop: good tyres on a dry road can decelerate a car at 8–9 m/s², close to the strength of gravity itself.
- A lift setting off: that brief heavy-in-the-knees moment is only about 1 m/s² — small, but your inner ear notices instantly.
- Cornering at a steady 25 m/s around a 125 m bend produces a centripetal acceleration of 5 m/s², aimed at the centre — constant speed, genuine acceleration.
- Your phone, constantly: its accelerometer chip senses accelerations to rotate the screen and count your steps. Physics in your pocket.
| Situation | Typical acceleration |
|---|---|
| Passenger lift setting off | ≈ 1 m/s² |
| Family car, brisk pull-away | ≈ 3 m/s² |
| Hard emergency braking, dry road | ≈ 8–9 m/s² |
| Free fall near Earth’s surface | 9.81 m/s² |
| Crewed rocket launch (held to ~3g for the crew) | ≈ 29 m/s² |
| Formula 1 car under heavy braking (~5g) | ≈ 50 m/s² |
Keep this table as a sanity check. If your homework answer says a pushbike accelerates at 60 m/s², it has just out-braked a Formula 1 car — go hunting for the slipped unit or sign.
Common Misconceptions About Acceleration
“Acceleration just means speeding up”
It means any change in velocity. Slowing down is acceleration directed against the motion, and turning is acceleration directed sideways. The speedometer can sit perfectly still while you accelerate around an entire roundabout.
“Zero velocity means zero acceleration”
A ball at the top of its throw is momentarily stationary, yet gravity accelerates it at 9.81 m/s² the whole time — which is precisely why it does not stay up there. Velocity describes the instant; acceleration describes the trend.
“Heavier objects fall faster”
Remove air resistance and a bowling ball and a feather accelerate identically at g. Heavier objects do feel a larger gravitational force, but they also need more force to accelerate — and the two effects cancel exactly.
“A negative acceleration always means slowing down”
The sign only tells you the direction relative to the axis you chose as positive. An object already moving in the negative direction with a negative acceleration is speeding up. Always read the sign against the velocity, never on its own.
How Acceleration Relates to Force and Newton’s Laws
So far we have described acceleration; Newton tells us what causes it — a net force. His second law is the bridge between the two ideas:
- F — net (resultant) force, in newtons (N)
- m — mass, in kilograms (kg)
- a — acceleration, in metres per second squared (m/s²)
Read it both ways. A larger net force means proportionally more acceleration; more mass means proportionally less — mass is, quite literally, resistance to being accelerated. One newton is defined as the force that accelerates 1 kg at exactly 1 m/s².
In practice the force you apply is rarely the net force: friction and air resistance push back, and only the leftover accelerates the object. For the full story, see our guides to Newton’s second law and all three of Newton’s laws of motion.
Worked Problems
These climb from the bare definition up to a force calculation. Cover the solutions and attempt each one first — that is where the learning happens.
