Acceleration
Acceleration is how fast velocity changes:
- Speeding up
- Slowing down (also called deceleration)
- Changing direction
- etc
It is usually shown as:
m/s2
"meters per second squared"
What is this "per second squared" thing? An example will help:
A runner accelerates from 5 m/s (5 meters per second) to 6 m/s in just one second
So they accelerate by 1 meter per second per second
See how "per second" is used twice?
It can be thought of as (m/s)/s but is usually written m/s2
So their acceleration is 1 m/s2
The formula is:
Acceleration = Change in Velocity (m/s) Time (s)
Example: A bike race!
You are cruising along in a bike race, going a steady 10 meters per second (10 m/s).
Acceleration: Now you start cycling faster! You increase to 14 m/s over the next 2 seconds (still heading in the same direction):
Your speed increases by 4 m/s, over a time period of 2 seconds, so:
Acceleration = Change in Velocity (m/s) Time (s)
= 4 m/s 2 s = 2 m/s2
Your speed changes by 2 meters per second per second.
Or more simply "2 meters per second squared".
Example: You are running at 7 m/s, and skid to a halt in 2 seconds.
You went from 7 m/s to 0, so that is a decrease in speed:
Acceleration = Change in Velocity (m/s) Time (s)
=
−7 m/s
2 s
= −3.5 m/s2
We don't always say it, but acceleration has direction (making it a vector):
A car is heading West at 16 m/s.
The driver flicks the wheel, and within 4 seconds has the car headed East at 16 m/s.
What is the acceleration?
The numbers are the same, but the direction is different!
Acceleration = Change in Velocity (m/s) Time (s)
Acceleration = From 16 m/s West to 16 m/s East 4 s
From 16 m/s West to 16 m/s East is a total change of 32 m/s towards the East.
Acceleration = 32 m/s East 4 s = 8 m/s2 East
For more complicated direction changes read vectors.