Math 153 Concept Check 22 Problem 1) The function t) = represents the position of an object moving counterclockwise around a circle of radius R. (a) Calculate the velocity function f" '(t). (a) Calculate the speed function l\"? '(t)| and confirm that the speed is always constant, | \"F '(t) | = Ra. (Hint: Use Pythagorean identity!) (You can assume R and a are both positive.) Problem 2) If velocity is the derivative of position, then position is an antiderivative of velocity. If acceleration is the derivative of velocity, then velocity is an antiderivative of velocity. An object's acceleration at time t is given by the vector-valued function (Ht) = . (a) Assume that the object's initial velocity (velocity at time t = 0) is 1'50 = . Find a vector-valued function 1'50?) representing the object's velocity at time t. (b) Assume that the object's initial position is F0 = . Find a vector-valued function t) representing the object's position at time t