When the velocity of an object remains constant, its average velocity is equal to the instantaneous velocity, and both remain constant over time (position is given in centimeters and time is given in seconds). This is precisely why we can use the following definition of average velocity:

v_avg = Δx/Δt

to describe the motion of an object moving at a constant velocity. We rewrite this equation as x = x₀ + v (t - t₀). But what happens when an object is not moving at a constant velocity?

While we won't get into a full discussion of why things move until Chapters 4 and 5 (Newton's laws), we can still use the concept of average velocity to describe the motion of an object. The animation shows a toy Lamborghini traveling at a nonconstant velocity.

What is the Lamborghini's average velocity, v_avg, in the time interval between t = 5 s and t = 10 s? It is still the displacement divided by the time interval, but how can we see this graphically?

Click the "show rise and run" button and then the "show slope" button. During this time interval (between 5 s and 10 s) the rise is the displacement and the run is the time interval; therefore, the slope of the line segment joining the points [x(5), 5] and [x(10), 10] represents the average velocity in this interval. An object beginning at [x(5), 5] would arrive at [x(10), 10] if it moved with the constant velocity represented by the slope of the line connecting those two points. Note that the notation [x(5), 5] describes the point on the graph at t = 5 s.