Final answer:
The correct answer is that velocity is not necessarily related to acceleration being zero, as you can have a nonzero velocity when acceleration is zero. This is shown by finding the velocity function v(t) from s(t), and then finding the acceleration function a(t), which is set to zero to find the specific time value. The velocity at this time value is nonzero.
Step-by-step explanation:
The question pertains to the concept of kinematics in physics, specifically velocity and acceleration in one-dimensional motion. In the provided function s(t) = x³ - 6x² - 11x + 30, we can find the velocity function by differentiating the position function with respect to time t, which gives us v(t) = 3x² - 12x - 11. To find when acceleration is zero, we differentiate the velocity function once more to get the acceleration function a(t) = 6x - 12, which equals zero when x = 2.
Then, we substitute x = 2 into the velocity function to find the velocity at the point where acceleration is zero: v(2) = 3(2)² - 12(2) - 11 = 12 - 24 - 11 = -23. Therefore, the velocity is not zero; it is -23 units (considering the units given with the function). Thus the correct answer to the question would be that velocity is not necessarily related to acceleration being zero, as acceleration can be zero at a point where velocity is non-zero.