A particle moves along the x-axis with position $$x(t) = 4\sin(\pi t)$$, where $$x$$ is in meters and $$t$$ is in seconds. What is the instantaneous acceleration at $$t = 0.25$$ seconds?

Two different representations of the same motion are given: (1) a position function x(t) = 5t² - 2t³ and (2) a velocity-time graph showing v = 0 at t = 0 and t = 5/3. What can be concluded about the object's motion?

A ball is attached to a spring and oscillates horizontally on a frictionless surface. If the position-time graph is sinusoidal, what can be concluded about the ball's acceleration?