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 velocity and the acceleration. If the current position of the object at time t is 3 {t}, then the position at time h later is 3 {t + h). The average velocity [speed] during that additional time 3 t+h 3 t Mgr gin is. the derivative 5' {t}. Use this function in the model below for the velocity function 1) {t}. . If we wa nl to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h } CI, 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} = y' (t) = s" {t}. Problem Set question: A particle moves according to the position function .913} = eat sin [t]. Enclose arguments of functions in parentheses. For example, 51119:]. to] Find the velocity function. um= as {b} Find the acceleration function. am= @E