To find when instantaneous velocity equals average velocity during a 10-second trip, the position function is given as s(t) = 3t² - 3t + 5 cm. The instantaneous velocity is calculated as s'(t) = 6t - 3. To determine the average velocity, one must compute the total change in position over the time interval, which is the difference in position at t=10 seconds and t=0 seconds divided by 10. The average velocity is found to be 57 cm/s, and the goal is to find a time t where the instantaneous velocity matches this value. It is essential to avoid posting the same problem in multiple forums to prevent confusion.
