A locomotive enters a station with an initial velocity of 19 m/s and slows down at a rate of .8m/s^2 as it goes through. If the station is 175 m long, how fast is it going when the nose leaves the station?

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Muscardinus Muscardinus · Answer 1 · 2019-07-04T11:15:56+02:00

Answer:

Final velocity, v = 25.3 m/s

Explanation:

Initial velocity of a locomotive, u = 19 m/s

Acceleration of the locomotive, a = 0.8 m/s²

Length of station, d = 175 m

We need to find its final velocity (v) when the nose leaves the station. It can be calculated using the third law of motion :

[tex]v^2-u^2=2ad[/tex]

[tex]v^2=2ad+u^2[/tex]

[tex]v^2=2\times 0.8\ m/s^2\times 175\ m+(19\ m/s)^2[/tex]

[tex]v^2=(641)\ m^2[/tex]

v = 25.31 m/s

v = 25.3 m/s

When the nose leaves the station, it will move with a velocity of 25.3 m/s. Hence, this is the required solution.