A 120-kg roller coaster cart is being tested on a new track, and a crash test dummy is loaded into it. The roller coaster starts from rest at point A which is 35m above the ground. The cart observed is to roll down the track to point B, which is 10 m above the ground. In your own words, what physics idea would you be able to use to predict how fast the cart is moving at point B?

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".