The movement of objects can be described using motion graphs and numerical values. These are both used to help in the design of faster and more efficient vehicles.
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:
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.
