i1 3. A body is coasting to a stop and the only force acting on it is a resistance proportional to its speed, according to the '3; t _ equation $1 = vJr = on e [m] ; 3(0) = 0, where on is the body's initial velocity (in m/ s), "r is its final velocity, m is its mass, it is a constant, and t is time. l- .I (a) If a body with mass m = 50 kg and k : 1.5 kg/ sec initially has a velocity of 30 m/s, how long, to the nearest sec- ond, will it take to slow to 1 m/s? (b) How far, to the 10 nearest meters, will the body coast during the time it takes to slow from 30 m/s to 1 m/s? (c) If the body coasts from 30 m/s to a stop, how far will it coast? 4. U(t) 3 Velocity (Kph) 8 HM DD 24 681012141618 Time (Hours) Three trains, A, B, and C each travel on a straight track for 0 S t g 16 hours. The graphs above, which consist of line segments, show the velocities, in kilometers per hour, of trains A and B. The velocity of C is given by UH) = 8t - 0.25i2 (Indicate units of measure for all answers.) (a) Find the velocities of A and C at time t = 6 hOurs. (b) Find the accelerations of B and C at time t = 6 hours. (c) Find the positive difference between the total distance that A traveled and the total distance that B traveled in 16 hours. ((1) Find the total distance that C traveled in 16 hours. The figure above shows the graph of 30:), where g is the derivative of the function f, for 3 g x g 9. The graph consists of three semicircular regions and has horizontal tangent lines at x = 0, x = 4.5, and x = 7.5. (a) Find all values of x, for 3