A motorboat cuts its engine when its speed is vi = m/s and then 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 at t = 0, and c is a constant. At t = s, the speed is v = m/s.
(a) Find the constant c.
(b) What is the speed at t1 = s?
(c) Differentiate the expression for v(t) and thus show that the acceleration of the boat is proportional to the speed at any time.