Acceleration

Acceleration is the change in speed or velocity of an object over a certain time. It can be calculated by dividing the change in velocity by the total time.

Acceleration is the rate of change in speed (or velocity).

It is defined as follows:

In physics, the following standard symbols are used to represent the quantities shown in the acceleration equation:

u – initial speed

v – final speed

a – acceleration

t - time

to give the final speed of an object after it has accelerated.

Acceleration is measured in metres per second per second ( m.s^-2 ), often pronounced as 'metres per second squared'.

Sometimes when we are describing motion we use the term 'constant speed'.

An object is travelling at a constant speed when its instantaneous speed has the same value throughout its journey. For example, if a car is travelling at a constant speed the reading on the car's speedometer does not change. The speedometer displays the speed of the car at each moment in time throughout the car's journey. In cases like this, where the motion involves only constant speed, the instantaneous speed of the object can be worked out using the relationship:

Speed = distance travelled/time taken

We also sometimes refer to a moving object as having a 'constant acceleration' or a 'uniform acceleration'. A constant or uniform acceleration means that the speed of the object changes by the same amount every second.

When the speed of an object is decreasing with time (i.e. slowing down), the object's speed is changing and so, by definition, the object is accelerating. If the velocity of an object is decreasing, the acceleration calculated will be negative.

This is sometimes known as a deceleration.

Example question:

Find the acceleration of a car, if it starts at 10 m/s and it reaches 30 m/s in 4 seconds.

The change in velocity is v – u, which is 30 – 10 = 20 m/s.

The acceleration is the change in velocity ÷ time, which is 20 m/s ÷ 4 s = 5 m/s².

What happens if the car slows down? Can you work out the acceleration now?

Find the acceleration of the car, if it starts at 20 m/s and it reaches 12 m/s in 2 seconds.

The change in velocity is v – u, which is 12 – 20 = -8 m/s.

The acceleration is the change in velocity ÷ time, which is -8 m/s ÷ 2 s = -4 m/s².

A minus sign means that the car is decelerating.

Acceleration and velocity

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:

• acceleration (α) is measured in metres per second squared (m/s²)
• change in velocity (∆v) 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).  This is also known as retardation. 

Example question:

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 = (28 - 0) = 28 m/s

α = Δv/t