Freight trains can produce only relatively small accelerations. (a) what is the final velocity of a freight train that accelerates at a rate of 0.0500m/s2 for 8.00 min, starting with an initial velocity of 4.00 m/s? (b) if the train can slow down at a rate of 0.550m/s2, how long will it take to come to a stop from this velocity? (c) how far will it travel in each case?

Under the action of a constant force an object accelerates at 7.8 m/s2. what will the acceleration be if (a) the force is halved? (b) the object's mass is halved? (c) the force and the object's mass are both halved? (d) the force is halved and the object's mass is doubled?

The radius of a sphere is increasing at a rate of 9 cm/ sec. find the radius of the sphere when the volume and the radius of the sphere are increasing at the same numerical rate.

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit