SOLUTION: Modern oil tankers weigh over a half-million tons and have lengths of up to one-fourth mile. Such massive ships require a distance of 4.3 km (about 2.7 mi) and a time of 16 min to

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Question 1205775: Modern oil tankers weigh over a half-million tons and have lengths of up to one-fourth mile. Such massive ships require a distance of 4.3 km (about 2.7 mi) and a time of 16 min to come to a stop from a top speed of 32 km/h.
(a) What is the magnitude of such a ship's average acceleration in m/s2 in coming to a stop?
(b) What is the magnitude of the ship's average velocity in m/s?

Answer by ikleyn(52775) About Me  (Show Source):
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Modern oil tankers weigh over a half-million tons and have lengths of up to one-fourth mile.
Such massive ships require a distance of 4.3 km (about 2.7 mi) and a time of 16 min
to come to a stop from a top speed of 32 km/h.
(a) What is the magnitude of such a ship's average acceleration in m/s2 in coming to a stop?
(b) What is the magnitude of the ship's average velocity in m/s?
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(a)  This motion is uniform deceleration with constant deceleration.

     Let "a" be the value of the constant deceleration.


     From Physics (Mechanics and Kinematics), having given the initial speed of 32 km/h
     and time 16 minutes to stop, we can calculate the average deceleration

         a = 32%2F%28%2816%2F60%29%29 = %2832%2A60%29%2F16 = 2*60 = 120 km/h^2.


     Here the ratio 16%2F60 is the time of 16 minutes converted to hours.

     Converted to m/s^2, this value of 120 km/h^2 is  

         %28120%2A1000%29%2F%283600%2A3600%29 = 12%2F%2836%2A36%29 = 1%2F%283%2A36%29 = 1%2F108 m/s^2 = 0.00926 m/s^2  (rounded).

     This value  0.00926 m/s^2 is the answer (average deceleration in m/s^2) for part (a).



(b)  The speed is linear function of time in this motion.

     The maximum value of the speed is 32 km/h; the minimum value is 0 km/h, when the ship stops.

     The magnitude of the ship's average velocity in km/h is  32%2F2 = 16 km/h,

     or  %2816%2A1000%29%2F3600 m/s = 16000%2F3600 m/s = 160%2F36 = 40%2F9 m/s = 44%2F9 m/s = 4.44444 m/s (rounded).

     This value  44%2F9 = 4.44444 m/s is the answer (ship's average speed in m/s) for part (b).

Solved.