Acceleration is change, not speed
A jet cruising at 900 km/h in a straight line has zero acceleration. A car pulling away from a traffic light at walking pace has a lot of it. That surprises people, because in daily life “accelerating” sounds like “going fast”. In physics it means something precise:
Acceleration is how much your velocity changes every second.
Say it out loud: “acceleration equals the change in velocity divided by the change in time.”
Acceleration· measured in m/s² (metres per second, per second)
How many m/s your velocity gains each second.
Change in velocity· measured in m/s
Final velocity minus starting velocity.
Time taken· measured in s
How long the change took.
See it happen
A car on a road with a position-versus-time and a velocity-versus-time graph below it. Set the starting velocity (and, in the acceleration version, the acceleration), then press Play to watch the car move and the graphs draw. Readings show time, position and velocity.
Accelerating car
InteractiveThe math, with your numbers
Try this
- →Set v₀ = 0 and a = +1. Look at the snapshots: why do the gaps keep growing?
- →Set v₀ = +6 and a = −1.5. The car brakes, stops… and then what?
- →Compare the two graphs: the velocity graph is a straight line, the position graph is a curve. Why?
Make a prediction first
Set v₀ = +6 m/s and a = −1.5 m/s². What happens after the car stops?
Think about it, then click to reveal the answer.
Make a prediction first
Set v₀ = +6 m/s and a = −1.5 m/s². What happens after the car stops?
Think about it, then click to reveal the answer.
It starts going backwards! Negative acceleration means the velocity keeps decreasing — through zero and into negative values. Acceleration doesn't “know” the car has stopped. (A real braking car stops because the brakes' force disappears when the wheels stop — a detail we'll see with forces.)
Two equations that predict the future
If the acceleration stays constant, we can predict exactly where the car will be and how fast it will go at any time. First, velocity — this one is just the definition of acceleration, rearranged:
Say it out loud: “the velocity now equals the starting velocity plus the acceleration times the time.”
Starting velocity· measured in m/s
The velocity at t = 0. The little 0 means 'initial'.
Velocity gained· measured in m/s
Gain a every second, for t seconds.
Position is trickier, because the velocity is changing the whole time. Here's the beautiful trick that solves it: the distance travelled equals the area under the velocity–time graph.
A velocity–time graph of a car that starts at speed v₀ and speeds up steadily with acceleration a. The shaded area under the line, up to time t, equals the distance travelled. Use the sliders to change v₀, a and t; the readings and the math panel below show the area and distance.
Distance = area under the velocity graph
InteractiveThe math, with your numbers
Deriving the position formula from the area
Step 1 of 3- 1The rectangle: height v₀, width t.
Worked example: a car from rest at 3 m/s² for 4 s
Step 1 of 3- 1Write what you know: v₀ = 0 (starts at rest), a = 3 m/s², t = 4 s.
Acceleration you can feel
You can't feel velocity — you're moving at about 30 km per second around the Sun right now, and you feel nothing. But you can feel acceleration: it's the push into your seat when a plane takes off, or the lurch when a bus brakes.
Wrap-up
Key ideas to remember
- Acceleration is the rate of change of velocity: , in m/s².
- Constant acceleration: velocity graph is a straight line; position graph is a curve (parabola).
- Distance travelled = area under the velocity–time graph. (Strictly it's the displacement: if the object reverses, area below the time axis counts as negative.)
- Predict the future: and .
Check your understanding
Sources & further reading
Everything in this lesson agrees with these references. They're all free to read.