If you are driving a car and your speed increases steadily from 20 km/h to 60 km/h over a specific time, your average speed during that period is simply the middle value, which is 40 km/h.

In uniform acceleration, the velocity increases linearly over time. The average velocity $v_{avg}$ is defined as the total displacement divided by the total time. Under uniform acceleration, the displacement $s$ is given by $s = \frac{u+v}{2} \times t$. Dividing this displacement by the time interval $t$ yields the average velocity $v_{avg} = \frac{u+v}{2}$.

Remember that $v_{avg} = \frac{u+v}{2}$ is only a shortcut for constant acceleration; for non-uniform motion, always use $v_{avg} = \frac{\Delta x}{\Delta t}$.