Question

A Metra train is at rest at the train station. You are running with a constant speed of `4.0m/s`. When you are 7.50m from the back end of the train, the train begins accelerating away from you at `0.12m/s^2`. Can you catch the train?

If so, when do you catch the train? If not, how close do you get?

Answer 1

yes

Explanation:

how much time takes the train to attain a speed of 4m/s? from the kinetic equation
`v= a xx t`
you have
`t= v/a= (4 m/s) / (0,12 m/s^2)= 33,3s`
now what distance that do you run in 33 s?
`s= v xx t = 4m/s 33,3s= 133,3 m`
How much is the distance that does the train run in that time?
`s= 1/2 a xx t^2= 1/2 xx 0,12 m/s^2 xx (33,3s)^2= 66,5 m`
since the train travels 66,5 m and you 133,3 m and it is only 7,5 m far, you can catch the train.
But the doors are correctly closed and you can't