Velocity is defined as the **rate of change of displacement over time.**

As with speed we can calculate both the average velocity over a period of time or the instantaneous velocity.

Velocity is a vector quantity ie it has magnitude and direction.

**v = Δs/Δt**

- v = velocity - in metres (ms
^{-1}) - s = displacement - in metres (m)
- t = times taken for displacement - in seconds (s)

Consider the same journey from Manchester to London used in the previous example. However this time we are interested in average velocity across Birmingham so we will be considering the straight line distances rather than total distance travelled

Using the displacement and times measured from Manchester

v_{ave}= Δs/Δt

Change in displacement = s_{2}-s_{1}

Change in time = t_{2}-t_{1}

v_{ave} = (s_{2}-s_{1})/(t_{2}-t_{1})

As with example for speed then if we take the reference point from when the vehicle first reaches Birmingham the equation is simplified and
the Δ symbols are often omitted

v_{ave} = s/t

**Example 1**

An object is moving with constant velocity.

If it's displacement from a reference position is is 20m when the time is 2 seconds and increases to 34m when the time is 9 seconds.

What is it's velocity?

s1 = 20m

s2 = 34ms

t1 = 2s

t2 = 9s

v= Δs/Δt

v = (s2 - s1)/(t2 - t1) = 14/7 = 2ms^{-1}

**Example 2**

The displacement of an object from a reference point increases by 3m in 6 seconds. What is its velocity?

s = 3ms

t = 6s

v_{ave}= s/t

v_{ave} = 3/6 = 0.5ms^{-1}

Note: because we do not know from the question 2 whether the velocity is constant we can only claim to know the average velocity!