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X Southern New Hampshire University - estion 8: (6 points) 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 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, i.e. the derivative s' (t) . Use this function in the model below for the velocity function v (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) = ' (t) = $" (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) =