The coordinate of an object is given as a function of time by x = 4t² - 3t³, where x is in meters and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is: A) -4 m/s² B) 4 m/s² C) -10 m/s² D) 10 m/s² E) -13 m/s²

Question

Quizplus · Accepted Answer

To find the average acceleration over the interval from t = 0 to t = 2 s, we need to find the change in velocity over that time interval and divide by the time interval. The velocity of the object is the first derivative of its position with respect to time: v(t) = 4² - 3³ Taking the derivative again to find acceleration: a(t) = 4⁰ - 3⁰ = 1⁰ Note that this acceleration is constant over the entire time interval from t = 0 to t = 2 s, so the average acceleration is just a(t) at any point within that interval. Therefore, the average acceleration is: a = 1 m/s⁰ However, we need to express the answer in the format given, so we simplify: a = 1 m/s⁰ = 10 m/s² Therefore, the best choice is (C).

The Coordinate of an Object Is Given as a Function