In the previous Problem Set question, we started looking at the position function 3 (t), the position of an object at time t . Two important physics concepts are the velocity 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 s t h. s t h ,5 l l + I: ( )) i.e. the derivative 3" (t). Use this function in the model below for the velocity function 'u (t). . If we want to analyze the instantaneous velocity at time 1!, this can be made into a mathematical model by taking the limit as h > O, 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) : 1.:Ir (t) : s" (t). Problem Set question: A particle moves according to the position function 3 (t) : n96t sin {5t}. Enclose arguments of functions in parentheses. For example, sin (2t). [a] Find the velocity function. a glalwsmta) no v(t)= (b) Find the acceleration function. a Elalwsinta) lino