The position function of an object moving along a straight line is given by s =

Question

The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of fat a. The position of a car at any time t is given by s = f(t) = 1/4t^2, 0 less than equal to t less than equal to 10, where s is given in feet and t in seconds. (a) Find the average velocity of the car over the time intervals [3, 4], [3, 3.5], [3, 3.1], [3, 3.01], and [3, 3.001]. [3, 4] ft/s [3, 3.5] ft/s [3, 3.1] ft/s [3, 3.01] ft/s [3, 3.001] ft/s (b) Find the velocity of the car at t = 3. ft/s

Explanation / Answer

[3,4] :
s(4) - s(3) / 4 - 3
1.75/1
1.75

[3 , 3.5] :
s(3.5) - s(3) / 3.5 - 3
1.625

[3 , 3.1] :
s(3.1) - s(3) / (3.1 - 3)
1.525

[3 , 3.01] :
s(3.01) - s(3) / (3.01 - 3)
1.5025

[3 , 3.001] :
(s(3.001) - s(3)) / (3.001 - 3)
1.50025

b)

As can be seen, with reducing intervals, the velocity comes to 1.5

So, 1.5 --> answer

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