A skateboard is rolling across a flat horizontal surface. Suppose the effect of friction is give by the differential equation: dv/dt--kv^(3/2) a. Suppose the skateboards initial velocity is 100 ft/min and that after four minutes, the skateboard has slowed down to 25 ft/min. Solve the differential equation to find a formula for the velocity of the skateboard at time t. b. Integrate your answer from part a to find a formula for the position of the skateboard at time t. (Assume that its initial position is 0.) c. Show that the skateboard will only travel a finite distance. What is that distance?