Preview Activity 7.1.1. The position of a moving object is given by the function 5(t), where 5 is measured in feet and t in seconds. We determine that the velocity is v(t) = 4t + 1 feet per second. a. How much does the position change over the time interval [0, 4]? b. Does this give you enough information to determine 5(4), the position at time t = 4? If so, what is 5(4)? If not, what additional information would you need to know to determine 5(4)? Iter 7 Di'erential Equations c. Suppose you are told that the object's initial position 5(0) = 7. Determine 5(2), the object's position 2 seconds later. d. If you are told instead that the object's initial position is 5(0) = 3, what is 5(2)? e. If we only know the velocity v(t) = 4t + 1, is it possible that the object's position at all times is 5(t) = 2t2 + t 4? Explain how you know. f. Are there other possibilities for 5(t)? If so, what are they? g. If, in addition to knowing the velocity function is v(t) = 4t + 1, we know the initial position 5(0), how many possibilities are there for 5(t)