# Velocity and acceleration

The of an object is its speed in a particular direction. Velocity is a quantity because it has both a magnitude and an associated direction. To calculate velocity, is used in calculations, rather than distance.

Unlike distance, which is a scalar quantity, displacement is a vector quantity. It includes:

• the distance travelled, measured in a straight line from start to finish
• the direction of the straight line

### Acceleration

When people run, fall, cycle or travel in a car or a plane their speed will change. They may speed up - , or slow down - . 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:  The average acceleration of an object can be calculated using the equation:  This is when:

• acceleration (a) is measured in metres per second squared (m/s²)
• change in velocity (∆v) is measured in metres per second (m/s)
• time taken (t) for the change in velocity is measured in seconds (s)

If an object is slowing down, it is decelerating (and its acceleration has a negative value). Some typical values for acceleration in metres per second (m/s²) include:

Method of travel Typical acceleration in m/s²
Running from a standing start6
Family car overtaking another car on a motorway4
Skydiver falling under the action of gravity10
Rollercoaster going into a loop 30 - 60
Race car leaving the starting grid in a race14

### 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) = (28 – 0) = 28 m/s   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) = (30 – 20) = 10 m/s   Question

A bicycle is moving at 10 m/s when the rider applies the brakes and stops in 5 seconds. What is the acceleration?

final velocity, (v) = 0 m/s

initial velocity, (u) = 10 m/s

change in velocity, (∆v) = (0 − 10) = -10 m/s   The answer is a negative acceleration so the bicycle is decelerating.