Acceleration
Rate of change of velocity.
Formula
Variables
Example
Speeding from 0 to 20 m/s in 4 s: a = 20/4 = 5 m/s².
How it works
This formula tells you how quickly an object's velocity is changing over a period of time. It works because acceleration is defined as the change in velocity divided by the time taken, so a bigger change in velocity or a shorter time gives a larger acceleration. Since velocity includes both speed and direction, acceleration can happen even if speed stays the same, as long as direction changes.
When to use it
Use this when you know an object's initial and final velocity and the time interval between them. It is common in motion problems for cars, balls, bicycles, elevators, and any situation where you need to find how strongly something speeds up or slows down.
Worked example, step by step
A cyclist increases velocity from 6 m/s to 14 m/s in 4 s. Step 1: Find the change in velocity: Δv = 14 - 6 = 8 m/s Step 2: Use the formula a = Δv / t Step 3: Substitute the values: a = 8 / 4 Step 4: Calculate: a = 2 m/s² Final answer: The cyclist's acceleration is 2 m/s².
Common mistakes to avoid
- using final velocity instead of change in velocity
- forgetting to subtract the initial velocity from the final velocity
- leaving the time unit out or using seconds incorrectly
Did You Know?
Acceleration is any change in velocity — speeding up, slowing down, OR turning all count.
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