Solving Bullet Train Speed Change Problem

[physics_learn]

I need some help with this question:

Two people, who are traveling on a bullet train between Tokyo and Kyoto, are willing to tolerate acceleration magnitudes as large as 0.2 g. The driver wants to change speeds from 250 to 300 km hr-1 on a curved piece of track. If the radius of curvature of the piece of track is 5 km, what is the minimum time the driver can use to change speeds?

For this question I am assuming that the angular acceleration is constant and that at the point where the tangential velocity is maximum (300Km/hr) the acceleration is 0.2g. I know I will get a smaller time if I consider the total acceleration to be the same during the whole trip. Any suggestions on how to solve this problem.

Thank you

 

[Hootenanny]

I need some help with this question:

Two people, who are traveling on a bullet train between Tokyo and Kyoto, are willing to tolerate acceleration magnitudes as large as 0.2 g. The driver wants to change speeds from 250 to 300 km hr-1 on a curved piece of track. If the radius of curvature of the piece of track is 5 km, what is the minimum time the driver can use to change speeds?

For this question I am assuming that the angular acceleration is constant and that at the point where the tangential velocity is maximum (300Km/hr) the acceleration is 0.2g. I know I will get a smaller time if I consider the total acceleration to be the same during the whole trip. Any suggestions on how to solve this problem.

Thank you

The first thing to point out is that the angular acceleration is not constant. I would start by writing down an equation the represents the condition given in the question, namely that the total acceleration cannot exceed 0.2g.

 

[physics_learn]

If I don't consider the angular acceleration constant, I believe that I end up with a differential equation, which I haven't been taught!
Please let me know if there is another approach I can take to this question

 

[Hootenanny]

If I don't consider the angular acceleration constant, I believe that I end up with a differential equation, which I haven't been taught!
Please let me know if there is another approach I can take to this question

You do indeed end up with an ODE, but it can be fairly easily solved and only really requires basic calculus knowledge. I'm afraid that if there is another way of doing it, I don't know of it.