1.An object thrown vertically upward from the surface of a celestial body reaches a height of f (t) = t² + 60t feet after t seconds on the interval [0,60]. Answer the following questions and justify by showing your work. Mark with appropriate units.

(a)What was the initial velocity of the object at t = 0?

(b) How many seconds did it take the object to reach its maximum height?

(c) Write a function a(t) that represents the object's acceleration for t seconds on the interval [0,60].

2. A bottle rocket is launched vertically and reaches a height of f(t) = -1/3t²+ 10t feet after t seconds on the interval [0,30]. Answer the following questions and justify by showing your work. Mark with appropriate units.

(a)Write a function v(t) that represents the bottle's velocity for t seconds on the interval [0,30].

(b)At what time t was the velocity of the bottle -6 feet/second?

(c)What is the bottle's speed at t = 20 seconds?