Please help solve and explain

In the previous Problem Set question, we started looking at the position function 5 (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 (3(t+h}:_3(t)) is. the derivative 3' (3). Use this function in the model below for the velocity function 1; (t). . If we want to analyze the instantaneous velocity at time 13, this can be made into a mathematical model by taking the limit as h > 0, 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 3 (t) = e8t sin (3t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. ab % '5 M 7r sin(a) [Ill 0 (b) Find the acceleration function. Va a sin (a) a (t =