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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) ) 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 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) = v (t) = s"(t). Problem Set question: A particle moves according to the position function s (t) = ett sin (8t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) : 4e^(4t) [sin(8t)+2cos(8t)] (b) Find the acceleration function