A driver traveling at 30 mph behind another car decides to pass it and presses the accelerator to the floor.

A driver traveling at 30 mph behind another car decides to pass it and presses the accelerator to the floor. Assuming that the accelerating behavior of the vehicle may be described by where v is the speed in ft/sec and t is the time in seconds.

dv / dt = 4-0.05v

where v is the speed in ft/sec and t is the time in seconds

a. Find the rate at which the vehicle is accelerating after 3 sec.

b. How long would it take the vehicle to reach a speed of 50 mph?