In the previous Problem Set question, we started looking at the position function s (f). the position of an object at time f. Two important physics concepts are the velocity and the acceleration. If the current position of the object at time i is s (), then the position at time h later is s (t + h). The average velocity (speed) during that additional time ha (o(+h)-54) If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h -+ 0, Le. the derivative s (t). Use this function in the model below for the velocity function u (f). The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a ($) can be modeled with the derivative of the velocity function, or the second derivative of the position function a (t) = v (t) = s" (f). Problem Set question: A particle moves according to the position function s (t) = eff sin (3t) Endose arguments of functions in parentheses. For example, sin (2#). [a) Find the velocity function. kin (a) [b) Find the acceleration function. Bin (a) O(0) = E