A crate falling from a plane is part of a closed system that has 24,450 J of mechanical energy. If the kinetic energy of the crate increases from 10,000 J
to 15,000 J, what happens to the gravitational potential energy of the system?

A. It decreases from 15,000 J to
10,000 J.

B. It decreases from 14,450 J to
9,450 J.

C. It increases from 10,000 J to
75,000 J.

D. It increases from 9,450 J to
14,450 J.

Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".