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)-8 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 time interval from t = 0 to t = 2 s, we need to find the change in velocity over that interval and divide by the time interval. The velocity at any time t is the derivative of the position function with respect to time: v = dx/dt = 4² - 3³ So the change in velocity over the interval from t = 0 to t = 2 s is: Δv = v(2) - v(0) = (4² - 3³) - (4⁰ - 3⁰) = 4² - 3² = ² So the average acceleration is: a = Δv/Δt = (²)/(2 - 0) = -10 m/s². Therefore, the answer is (C), -10 m/s².

The Coordinate of an Object Is Given as a Function