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 h is (s(tth)-s(t)) . 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, h 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) = v (t) = s" (t)- Problem Set question: A particle moves according to the position function s (t) = est sin (4t). Enclose arguments of functions in parentheses. For example, sin (2t)- (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) =