The position of an object moving along a straight line is given by x(t) = 4t³ - 3t² + 2t - 1, where x is in meters and t is in seconds. What is the average velocity of the object between t = 1 s and t = 3 s?

Core Concept

Average velocity is the change in position divided by the change in time. Calculate x(3) = 4(3)³ - 3(3)² + 2(3) - 1 = 108 - 27 + 6 - 1 = 86 m. Calculate x(1) = 4(1)³ - 3(1)² + 2(1) - 1 = 4 - 3 + 2 - 1 = 2 m. Average velocity = (86 - 2)/(3 - 1) = 84/2 = 34 m/s.