The tutor illuminates a very plain, yet critical, concept from physics.

Average velocity has the following definition:

v_ave=displacement/time

Displacement means your change in position. (Read more about the difference between distance and displacement in my post here.)

Travelling straight-line, displacement and distance are numerically equivalent, except that for displacement, going backwards is negative. Reporting displacement, direction need be included (North, for instance).

Let’s consider the situation of straight-line travel, but with velocity that is not consistent:

Example. A motorist travelling East drives for three hours at 80km/h, then stops for a 45 minute lunch, then continues East at 70km/h for another 40 minutes. What is the average velocity?

Solution:

We refer to the formula

v_ave=(sum of displacements)/(total time)

Using the formula

displacement=velocity x time

we can find the driver’s displacement along each leg of the journey, then add them. We divide that sum by the total travel time, including the break. Of course, the minutes need be converted to hours:

v_ave=(80×3 + 0x(45/60) + 70x(40/60))/(3 + 45/60 + 40/60) km/h East

which simplifies to

v_ave=286.67/4.42=64.9 km/h East

Due to breaks, and even stopping and starting, a person’s average velocity can be significantly less than their driving speed:)

Source:

Heath, Robert et al, Fundamentals of Physics. D.C. Heath Canada, Ltd, 1981.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.