At time t = 0 a car moves into the passing lane to pass a slow-moving truck. The average velocity of the car from t = 1tot = 1+his

v = 3 (h+1) 2.5 + 580h-3 ave 10h

Estimate the instantaneous velocity of the car at t = 1, where time is in seconds and distance is in feet.

The correct given equation is:

v = [3 (h + 1) ^2.5 + 580 h - 3] / 10 h

So to solve for the instantaneous velocity at t = 1, we must set h = 0. However we cannot do that since h is in denominator and a number divided by a denominator is infinite. Therefore we must set h to something almost zero. In this case, h = 0.0000001, so that:

at t = 1

v = [3 (0.0000001 + 1) ^2.5 + 580 (0.0000001) - 3] / 10 * 0.0000001

v = 58.75 ft/s