Acceleration

Acceleration 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).

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, acceleration, or slow down, deceleration.

Some typical values for acceleration in metres per second (m/s2) include:

Method of travelTypical acceleration (m/s²)
Running2
Family car1-7
Motorbike1-10
Rollercoaster30 - 60
Formula One car49

The acceleration in freefall due to the Earth's gravity is 10 m/s2.

g = 10 m/s2