In the previous Problem Set question, we started looking at the position function s (t), the position of an object at time t . Two important physics concepts are the veloocity and the acceleration. If the current position of the object at time t is s (t), then the position at time h later is s (t + h). The average velocity (speed) during that additional time his (s(tth)-s(t)) h . 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, i.e. the derivative s' (t). Use this function in the model below for the velocity function u (t)- The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a (t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a (t) = u' (t) = s" (#). Problem Set question: A particle moves according to the position function s (t) = edt sin (8t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. /a a sin (a) III ? w (t) =_ (b) Find the acceleration function. a sin (a) ? a(t) =5