Finding the time and speeds at which the front and back of a train pass a post.

Question

Hello,

I need help figuring out the following question: A train has a length of 44 m. The front of the train is 100 m from a post. It accelerates at 0.5 m/s^2.

a) What is the time interval between the front and back of the train passing the post?

b) What are the speeds at which the front and rear of the train pass the post?

Much appreciated!

Answer 1

I am assuming the train is starting from rest.

Looking at the front of the train, it needs to cover 100 meters to reach the post

using x = 0.5 a t² we get 100 = (0.5)(0.5)(t²) which gives a time of 20 seconds

The back of the train has the same acceleration but must cover 144 meters

We get 144 = (0.5)(0.5)(t²) which gives a time of 24 seconds

Therefore the time interval is 24-20 = 4 seconds

For the speed for the front we use v = (0.5)(20) = 10 m/s

For the back of the train we use v = (0.5)(24) = 12 m/s