Question

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?

Answer 1

Final velocity, v = 25.3 m/s

Step-by-step 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 :

`v^2-u^2=2ad`

`v^2=2ad+u^2`

`v^2=2* 0.8\ m/s^2* 175\ m+(19\ m/s)^2`

`v^2=(641)\ m^2`

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.