Basic kinematics variables using calculus: The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s²) t - (1.0 m/s³) t². Determine the instantaneous acceleration of the object at time t = 4.00 s. A) -2.00 m/s² B) -5.00 m/s² C) 1.00 m/s² D) 0.00 m/s² E) -1.00 m/s²

Question

Quizplus · Accepted Answer

To find the instantaneous acceleration, we need to find the derivative of the velocity function with respect to time. Taking the derivative of v(t) gives: a(t) = 3.00 m/s² - 2.00 m/s³ t At t = 4.00 s, we have: a(4.00) = 3.00 m/s² - 2.00 m/s³ (4.00) a(4.00) = -5.00 m/s² Therefore, the best choice is B, with an explanation that we found the instantaneous acceleration by taking the derivative of the velocity function and evaluated it at t = 4.00 s to get -5.00 m/s².

Basic Kinematics Variables Using Calculus: the Velocity of an Object