Question

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

Answer 1

`9m\/s`

Step-by-step explanation

Parameters given:

Initial velocity, u = 19 m/s

Acceleration, a = -0.8m/s² (the train is slowing down)

Distance traveled, s = 175 m

To find the final velocity of the train, we have to apply one of Newton's equations of motion:

`v^2=u^2+2as`

where v = final velocity

Substituting the given values into the equation, the final velocity of the train as its nose leaves the station is:

`\begin{gathered} v^2=19^2+(2\cdot-0.8\cdot175) \\ v^2=361-280 \\ v^2=81 \\ \Rightarrow v=\sqrt[]{81} \\ v=9m\/s \end{gathered}`

That is the answer.