Chapter 6.1, Problem 26E

Day hike The velocity (in mi/hr) of a hiker walking along a straight trail is given by $v\left(t\right)=3{\sin }^2\frac{\pi t}{2}$, for $0\le t\le 4$. Assume s(0) = 0 and t is measured in hours

  a.    Determine the position function, for $0\le t\le 4$. (Hint: ${\sin }^{2}t=\frac{1-{\cos }^{2}t}{2}$.)

  b.    What is the distance traveled by the hiker in the first 15 min of the hike?

  c.    What is the hiker’s position at t = 3?