A small ball swings in a horizontal circle at the end of a cord of length l1, which forms an angle θ1 with the vertical. The cord is then slowly drawn through the support at O until the length of the free end is l2. (a) Derive a relation among l1, l2, θ1, and θ2. (b) If the ball is set in motion so that initially l1 5 0.8 m and θ1 5 35°, determine the angle θ2 when l2 5 0.6 m.

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".