A motorboat cuts its engine when its speed is 11.7 m/s and coasts to rest. The e

Question

A motorboat cuts its engine when its speed is 11.7 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, v i, is the initial speed at t = 0, and c is a constant. At t = 17.7 s, the speed is 5.00 m/s. Find the constant c. Your response differs from the correct answer by more than 10%. Double check your calculations, s -1 What is the speed at t = 40.0 s? Your response differs from the correct answer by more than 10%. Double check your calculations, m/s Differentiate the expression for v(t) and thus show that the acceleration of the boat is proportional to the speed at any time. a = cv a = -cv a = cv i a = -ce -ct a = cv i e -ct a = ce-ct

Explanation / Answer

(a) 5 = 11.7*e^(17.7c) Solving this equation we get... c = 0.048 (b) At t= 40 sec , V= 11.7*e^(-0.048*40) = 1.715 m/s

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