Problem 2: Velocity and Speed {20 points} . . . . . . . . Tl't . . Suppose that an obJect moving along a straight line has position Function 5(t} = E sIn() t cos() In Feet. WIth 2 t '2 0 measured in seconds. a} (2 points} Show that the velocity function. v(t}, is equal to v(t) 2 3t sinGE-E). Since the answer for this part is given, it is especially important to show each step in your work. b} (4 points} Write a definite integral that gives the displacement of the object during the time interval [2. 5]. Then calculate the displacement. Integral: Displacement: l e. c} (3 points} Explain what 3- / v(t}dt represents. Then find its value. . 2 VALUE: d) (3 points} Write a definite integral that gives the total distance traveled of the object during the time interval [2.51. Then calculate the distance traveled. Integral: Distance Traveled: l 5 e} (3 points} Explain what if |v(t}| dt represents. Then find its value. 2 VALUE