# 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 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

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

$\Delta v = v - u$

The average acceleration of an object can be calculated using the equation:

$acceleration = \frac{change~in~velocity}{time~taken}$

$\alpha = \frac{\Delta v}{t}$

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).

### 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

$\alpha = \frac{\Delta v}{t}$

$a = 28 \div 8$

$\alpha = 3.5 m/s^2$

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 = (30 - 20) = 10 m/s

$\alpha = \frac{\Delta v}{t}$

$\alpha = 10 \div 25$

$\alpha = 0.4~m/s^2$