Acceleration
accelerationThe rate of change in speed (or velocity) is measured in metres per second squared. Acceleration = change of velocity Ă· 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).
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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 â 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 Ă· time taken., or slow down, decelerationSlowing down or negative acceleration, eg the car slowed down with a deceleration of 2 msâ»ÂČ..
Some typical values for acceleration in metres per second (m/s2) include:
| Method of travel | Typical acceleration (m/sÂČ) |
| Running | 2 |
| Family car | 1-7 |
| Motorbike | 1-10 |
| Rollercoaster | 30 - 60 |
| Formula One car | 49 |
| Method of travel | Running |
|---|---|
| Typical acceleration (m/sÂČ) | 2 |
| Method of travel | Family car |
|---|---|
| Typical acceleration (m/sÂČ) | 1-7 |
| Method of travel | Motorbike |
|---|---|
| Typical acceleration (m/sÂČ) | 1-10 |
| Method of travel | Rollercoaster |
|---|---|
| Typical acceleration (m/sÂČ) | 30 - 60 |
| Method of travel | Formula One car |
|---|---|
| Typical acceleration (m/sÂČ) | 49 |
The acceleration in freefall due to the Earth's gravity is 10 m/s2.
g = 10 m/s2