Example 3: Average Velocity With Respect to Time and Distance

A car travels with velocity v = 4t + 10, where t is time. Between times t = 0 and t = 4 find the average velocity with respect to (a) time, and (b) distance.

(a)       (Figure 6.5.5(a)).

(a)                                                              (b)

Figure 6.5.5

(b) Let s be the distance, and put s = 0 when t = 0. Since ds = v dt = (4t + 10)dt, at time t = 4 we have

Then

v_ave =

=

=

=

= ~ 19.2 (Figure 6.5.5(b)).