Acceleration
accelerationThe rate of change in speed (or velocity) is measured in metres per second squared. Acceleration = change of velocity ÷ time taken. is the rate of change of velocity. It is the amount that velocity changes per unit time.
If an object accelerates from an initial velocity (u) up to a final velocity (v) then the average acceleration of an object can be calculated using the equation:
\( acceleration = \frac{change \ in \ velocity}{time \ taken} \)
\( α = \frac{v - u}{t} \)
This is when:
- acceleration (α) is measured in metres per second squared (m/s2)
- change in velocity (v - u) is measured in metres per second (m/s)
- time taken (t) is measured in seconds (s)
If an object is slowing down, it is decelerating (and its acceleration has a negative value).
Learn more on acceleration in this podcast
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Example
A car takes 8.0 s to accelerate from rest to 28 m/s. Calculate the average acceleration of the car.
final velocity, v = 28 m/s
initial velocity, u = 0 m/s (because it was at rest – not moving)
change in velocity, v - u = (28 - 0) = 28 m/s
\( α = \frac{v - u}{t} \)
\( α = 28 \div 8\)
\( α = 3.5 \ m/s^{2}\)
Question
A car takes 25 s to accelerate from 20 m/s to 30 m/s. Calculate the acceleration of the car.
final velocity, v = 30 m/s
initial velocity, u = 20 m/s
change in velocity, v - u = (30 - 20) = 10 m/s
\( α = \frac{v - u}{t}\)
\( α = 10 \div 25\)
\( \alpha = 0.4 \ m/s^{2}\)
Typical accelerations
When people run, fall, cycle or travel in a car or a plane their speed will change. They may speed up, accelerationThe rate of change in speed (or velocity) is measured in metres per second squared. Acceleration = change of velocity ÷ time taken., or slow down, decelerationSlowing down or negative acceleration, eg the car slowed down with a deceleration of 2 ms⁻²..
Some typical values for acceleration in metres per second (m/s2) include:
| Method of travel | Typical acceleration (m/s²) |
| Running | 2 |
| Family car | 1-7 |
| Motorbike | 1-10 |
| Rollercoaster | 30 - 60 |
| Formula One car | 49 |
| Method of travel | Running |
|---|---|
| Typical acceleration (m/s²) | 2 |
| Method of travel | Family car |
|---|---|
| Typical acceleration (m/s²) | 1-7 |
| Method of travel | Motorbike |
|---|---|
| Typical acceleration (m/s²) | 1-10 |
| Method of travel | Rollercoaster |
|---|---|
| Typical acceleration (m/s²) | 30 - 60 |
| Method of travel | Formula One car |
|---|---|
| Typical acceleration (m/s²) | 49 |
The acceleration in freefall due to the Earth's gravity is 10 m/s2.
g = 10 m/s2
