If a ball is thrown into the air with a velocity of 100 ft/s, its height in feet after t seconds is given by LaTeX: h\left(t\right)=100t-16t^2h ( t ) = 100 t − 16 t 2 . Find the average velocity of the ball for the time period from t = 1 to t = 3.

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".