As a certain object falls, its position s (in meters) above ground after t secon

Question

As a certain object falls, its position s (in meters) above ground after t seconds is given by s(t) = 15 ? 5t2. (a) What is the average velocity of the object on the interval from t = 1 to the time 0.5 seconds later? (b) What is the average velocity of the object on the interval from t = 1 to the time 0.1 seconds later? (c) Write a polynomial in terms of h for the average velocity from t = 1 to the time h seconds later (h ? 0). (Simplify your answer completely.) (d) What does this average tend toward for h closer and closer to 0 (smaller and smaller time interval)? (e) What would you guess to be the exact velocity of the object after 1 second?

Explanation / Answer

v(t) = -10t ===> v(1) = -10 , v(1.5) -=10(1.5) = -15 ==> average velocity = [-15 -10]/0.5 = -12.5

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