EXAMPLE 3 Show that the average velocity of a car over a time interval [t,, t,] is the same as the average of its velocities during the trip. SOLUTION If s(t) is the displacement of the car at time t, then, by definition, the average velocity of the car over the interval is s ( t 2 ) - s ( t ) As At On the other hand, the average velocity function on the interval is 1 1 ave v(t) dt = s'(t) dt t, - tilt, t2 - tilt 1 t, - t -[s(t,) - s(t,)] (by the Net Change Theorem) s (t , ) - s(t ) S