The Legacy of Newton, Gallileo, and Leibniz: Quiz

Problem 3

Find the average velocity of the object whose position at time t is x(t) = (t2 + 3t)/(t + 1) for the time intervals given below.

  1. [0, 1]
  2. [0.5, 1]
  3. [0.9, 1]
  4. [0.95, 1]

Answers, problem 3

  1. Average velocity for [0, 1] = (x(1) - x(0))/(1-0) = (4/2 - 0/1)/1 = 2
  2. Average velocity for [0.5, 1] = (x(1) - x(0.5))/(1-0.5) = (4/2 - 7/6)/0.5 = 1.667
  3. Average velocity for [0.9, 1] = (x(1) - x(0.9))/(1-0.9) = (4/2 - 351/190)/0.1 = 1.526
  4. Average velocity for [0.95, 1] = (x(1) - x(0.95))/(1-0.95) = (4/2 - 1501/780)/0.05 = 1.513

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