A motorboat cuts its engine when its speed is 10.0 m/s and coasts to rest. The equation describing the motion of the motorboat during this period is v = vie-ct, where v is the speed at time t, vi is the initial speed, and c is a constant. At t = 20.0 s, the speed is 5.00 m/s. (a) Find the constant c. (b) What is the speed at t = 40.0s? (c) Differentiate the expression for v (t) and thus show that the acceleration of the boat is proportional to the speed at any time.