When will velocities of the trains equal?

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In summary, the problem involves two trains, A and B, with A moving at a constant velocity of x m/s and B starting from rest and accelerating at a constant rate. After 20 seconds, the two trains have traveled the same distance and B is moving faster than A. The question is at what time was B moving at the same speed as A.
  • #1
Entr0py
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Homework Statement


A train having a velocity of x m/s is caught by a train accelerating from zero 20 seconds after the second train starts. At what time were their velocities equal?

Homework Equations

The Attempt at a Solution


I was thinking that you'd have to assume that the train with x velocity is traveling with constant velocity and that the second train starts at t=t-20 s. However, I'm confused as to how I would find when their velocities would be equal.
 
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  • #2
How far does the first train travel?
 
  • #3
So in 20 s, the first train has traveled x=x0+v0t+.5at^2. well I assumed it started from rest, so x=.5a(400) or 200a m.
 
  • #4
I'd call that the second train from my reading of the problem statement. Let's tidy up the statement a bit so we're both discussing the same trains. "Train A is moving at a constant velocity of x m/s. As it pulls even with Train B, Train B accelerates from 0 at a constant rate, and pulls even with A after 20 seconds. At what time are the two velocities equal?"

Now, I ask how far does Train A travel?
 
  • #5
I'm sorry I'm confused?
 
  • #6
Entr0py said:
I'm sorry I'm confused?
You need to say exactly what is confusing you. Bystander's description of the problem is correct. I'll try to make it more concrete.
At t=0, both trains are at s=0. Train A is moving at constant speed x, train B is stationary.
Train B then accelerates at some unknown constant (we must assume) rate a. At t=20, the trains have traveled the same distance. Train B must now be moving faster than train A.
At what time was train B moving at speed x?

Bystander is asking you, first, how far train A traveled in those 20 seconds.
 

1. When will the velocities of the trains equal?

The velocities of the trains will equal when they are both traveling at the same speed or when their velocities are equal. This can occur at any point in time depending on various factors such as acceleration, distance, and initial velocities.

2. How do you calculate when the velocities of the trains will equal?

To calculate when the velocities of the trains will equal, you will need to know the initial velocities of each train, the acceleration of each train, and the distance between the two trains. Using these values, you can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Set the final velocities of both trains equal to each other and solve for t to determine the time when the velocities will be equal.

3. What factors can affect when the velocities of the trains will equal?

There are several factors that can affect when the velocities of the trains will equal. These include the initial velocities of the trains, the acceleration of each train, and the distance between the two trains. Other factors such as external forces and friction can also play a role in the equality of velocities.

4. Can the velocities of the trains ever be equal if they have different initial velocities?

Yes, the velocities of the trains can still be equal even if they have different initial velocities. This is because the acceleration of each train can cause their velocities to change over time, resulting in them eventually reaching the same velocity. However, the time it takes for this to occur will depend on the initial velocities and accelerations of the trains.

5. Is it possible for the velocities of the trains to never be equal?

Yes, it is possible for the velocities of the trains to never be equal. This can occur if the trains have significantly different initial velocities and/or accelerations, or if there are external factors that prevent them from reaching equal velocities. In some cases, the trains may never reach equal velocities but may come close to it without ever truly being equal.

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