Given information: An object is moving with velocity (in feet per second) described by the function v (t) = 4t + 1. We will reason about the object's position function, s (t). Question 1 How much does the position change over the time interval [0,4]? Recall: displacement = f v(t) dt Answer with a number only (units are feet). 36 Question 2 Question: Think back to the total change theorem. What additional information would allow us to find s(4), the object's position at time t Answer: We'd need to know the object's position at another time; for example s(0) Question 3 Suppose you are told that the object has initial position $(0) =3. What is s(2)? 3 = 4? 1 pts 1 pts 1 pts Question 4 Given information: A different object is moving with velocity (in feet per second) described by the function v(t) = 1 sin(t). The object has initial position s(0) = 6. People often assume that the object's position function would be s(t) = t + cos(t) +6 However, this is not right. Why not? We were given v(t) = 1 sin(t), but this function has derivative s' (t) = sin(t) + 6t - We were given s(0) = 6, but this function has initial value s(0) = 7. Actually, s(t) = t + cos(t) +6 is correct based upon both pieces of given information. Question 5 Given information: An object is moving with velocity (in feet per second) described by the function v(t) = e t. The object has initial position s(0) = 0. The object's position function is s(t) = e - 1 t k. What is the correct value of k? 1 pts 1 pts