Calculating Train Deceleration: Solving a Homework Problem in 4 Steps

[Milos Zivkovic]

Homework Statement

A person standing on a train platform notices that the first train car, which is approaching the station, had passed him in 4 seconds, and that the second train car passed him in 5 seconds. After this, the front of the train stopped at the distance of 75 meters from the person. Assuming the deacceleration of the train is constant, find its value.

The problem was translated, so I apologize for any mistakes.

Homework Equations

( V - Velocity, D - Distance, t - Time)
V = D/t
V= V_o + a*t
V²=V_o² +2a*D
D= V_o*t + at²/2
...

The Attempt at a Solution

I tried to solve it using integrals, but no luck. I am not sure how to break down this problem and solve it accordingly.

The answer should be: -0.25 m/s²

 

[Orodruin]

Please show your actual work.

 

[andrewkirk]

Integrals are not needed. It can be solved by simultaneous equations. Focus on the distance of the front of the train from the observer.

Choose some unknown quantities whose values we want to find - for instance L for the length of a carriage, a for the acceleration and u for the initial velocity when the front of the train passes the observer. However many unknowns you have, that's how many equations you need to be able to solve for them. For example, using the equations you wrote above, you should be able to write at least three equations, one for each of the following periods:
1. while first carriage is passing observer
2. while second carriage is passing observer
3. from end of second period to when train is stopped