Water is flowing in a trapezoidal channel at a rate of q = 20 m3/s. the critical depth y for such a channel must satisfy the equation 0=1-(q^2 b)/(ga_c^3 ) where g is gravity, ac is the cross-sectional area, and b is the width of the channel at the surface. for this case, the width and the cross-sectional area can be related to depth y by b = 3 + y and ac = 3y + 1/2y2. use initial guesses for the location of the root of a=0.5 and b= 2.5. the error on the solution should not exceed 1%.

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".