The function f(x) = 4t^3 - 57t^2 + 210t + 6 is the vertical location of an object where f is in ft and t is in sec.

1. Solve for an expression for the object's velocity.
2. Solve for an expression for the object's acceleration.
3. Solve for an expression for the object's speed.
4. Solve for its displacement during the beginning five secs.
5. Solve for its average velocity during the beginning five secs.
6. Solve for the instantaneous velocity where time is 2.
7. Solve for the acceleration of the object where time is 2.
8. For which values will the object change direction?
9. Solve for the acceleration each time the object changes direction.
10. Solve for the speed of the object when time is 3 secs.
11. Solve for the total distance the object travels over the beginning ten secs.