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, Le. the derivative s' (t). Use this function in the model below for the velocity function v () 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) - (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. U (t ) = (b) Find the acceleration function. a (t) =