Acceleration
Simple Explanation
Acceleration measures how quickly velocity is changing — the change in velocity per unit time. An object accelerates whenever it speeds up, slows down (decelerates), or changes direction.
Why Do We Need It?
Acceleration is what connects force to motion — it's the quantity that Newton's second law (F = ma) directly links to the forces acting on an object.
Formula
Acceleration
a = (v − u) / t
How quickly velocity is changing.
- a
- — acceleration, in metres per second squared (m/s²)
- v
- — final velocity, in m/s
- u
- — initial velocity, in m/s
- t
- — time taken for the change, in seconds (s)
When to use it: Whenever an object is speeding up, slowing down, or changing direction, and you need to measure the rate.
Worked Example
Calculate a car's acceleration
A car speeds up from 10 m/s to 30 m/s in 5 s. Find its acceleration.
Why Does This Work?
Dividing the total change in velocity by the time it took to change gives the average rate of that change per second — exactly what acceleration measures, in units of (m/s) per second, or m/s².
Real-Life Example
0–100 km/h times for cars
Car reviews often quote how many seconds a car takes to go from 0 to 100 km/h.
That figure is a direct, everyday measurement of acceleration — a smaller time means a larger (faster) acceleration.
Practice
A cyclist accelerates from 2 m/s to 8 m/s in 3 s. What is their acceleration?
EasyA ball decelerates from 12 m/s to 0 m/s in 4 s. What is its acceleration? (Include the sign.)
MediumCommon mistake
Assuming acceleration only means 'speeding up' — an object slowing down also has a (negative) acceleration, and an object changing direction at constant speed is accelerating too.
Quick Review
- acceleration = change in velocity / time = (v−u)/t
- Deceleration is just negative acceleration.
- Units are m/s².