Question

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.

Answer 1

The question is asking for the instantaneous velocity of a car at t = 1 second, which would normally be found by differentiating the position function. However, due to potential typos in the provided equation, the instantaneous velocity cannot be calculated directly.

Step-by-step explanation:

The problem asks for the instantaneous velocity of the car at time t = 1 second. To find the instantaneous velocity, we would typically take the derivative of the position function with respect to time. However, the given equation v = 3(h+1)2.5 + 580h - 3 ave 10h appears to have some issues, possibly due to typos, and cannot be processed as is. In general, if the average velocity function over time h was given correctly, we would evaluate the derivative of that function at h = 0 to find the instantaneous velocity at t = 1 second.

Answer 2

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