The first hill of a roller coaster is 42.0 meters high. The roller coaster drops to a height of 4.2 meters above the ground at the bottom of this first hill.

If the mass of the roller coaster is 34,500 kg, what is the velocity at the bottom of the first hill? Ignore friction and assume the velocity at the top of the first hill is 0 m/s.

A. 1,614 m/s
B. 9.1 m/s
C. 20.3 m/s
D. 27.2 m/s

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".