Acceleration is the rate of change of velocity. It is the amount that velocity changes per unit time.
The change in velocity can be calculated using the equation:
change in velocity = final velocity – initial velocity
The average acceleration of an object can be calculated using the equation:
This is when:
If an object is slowing down, it is decelerating (and its acceleration has a negative value).
A car takes 8.0 s to accelerate from rest to 28 m/s. Calculate the average acceleration of the car.
final velocity, = 28 m/s
initial velocity, = 0 m/s (because it was at rest – not moving)
change in velocity, = (28 – 0) = 28 m/s
= 28 ÷ 8
= 3.5 m/s2
A car takes 25 s to accelerate from 20 m/s to 30 m/s. Calculate the acceleration of the car.
final velocity, = 30 m/s
initial velocity, = 20 m/s
change in velocity, = (30 – 20) = 10 m/s
= 10 ÷ 25
= 0.4 m/s2
If an object moves along a straight line, its motion can be represented by a velocity–time graph. The gradient of the line is equal to the acceleration of the object.
The table shows what each section of the graph represents:
|Section of graph||Gradient||Velocity||Acceleration|
|D (v = 0)||Zero||Stationary (at rest)||Zero|
Scientists draw graphs of data to help analyse a situation. A velocity-time graph of a journey can give information about acceleration (the gradient) and distance travelled (displacement).
The area under the graph can be calculated by:
Calculate the total displacement of the object - whose motion is represented by the velocity–time graph below.
Here, the displacement can be found by calculating the total area of the shaded sections below the line.