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 5.1 km (about 3.2 mi) and a time of 18 min to come to a stop from a top speed of 34 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?


Respuesta :

(a) [tex]-1.46\cdot 10^{-4} m/s^2[/tex]

The average acceleration of the ship is given by

[tex]a=\frac{v-u}{t}[/tex]

where

v is the final velocity

u is the initial velocity

t is the time elapsed

Here we have:

[tex]u=34 km/h =9.44 m/s[/tex] is the initial velocity

v = 0 is the final velocity

[tex]t=18 min =64800 s[/tex] is the time elapsed

Substituting, we find

[tex]a=\frac{0-9.44 m/s}{64800 s}=-1.46\cdot 10^{-4} m/s^2[/tex]

(b) 4.72 m/s

Assuming the acceleration is uniform, the average velocity of the ship is given by:

[tex]v_{avg} = \frac{v+u}{2}[/tex]

where

v is the final velocity

u is the initial velocity

Here we have:

v = 0

u = 9.44 m/s

So the average velocity of the ship is

[tex]v_{avg} = \frac{0+9.44 m/s}{2}=4.72 m/s[/tex]