Help Needed: Solving Train Acceleration Problem

In summary: In this case, your origin should be the point at which each train begins its journey. You then need to determine the initial velocity of each train. For train A, the initial velocity is 39 m/s. For train B, the initial velocity is at rest. Next, you need to determine the acceleration of each train. For train A, the acceleration is 0.05 m/s^2. For train B, the acceleration is unknown. Finally, you need to determine the velocity of each train at some point in time. For train A, the velocity at some point in time is 39 m/s. For train B, the velocity at some point in time is unknown.
  • #1
Parallel
42
0
hello

I'm having some trouble with the following problem:

train B leaves point A at 8am to point B located 30 km straight a head.
the train has constant acceleration a=0.05 m/sec^2

now train B leaves point B 5 minutes before train A gets there,what is the acceleration of train B in order for the trains to meet with the same velocity?
(i.e will not collide)

I computed the speed of train A 5 min before it arrived to point B.
I know it's acceleration,but it seems I don't have enough information to solve the problem,I have 2 unknowns: train B's acceleration and the location they meet...but I have only one equation.

can someone please help me.
 
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  • #2
what is the initial velocity of A. What is its acceleration?
what would be its velocity at some t while it traveling along the track?
Write an equation using the above knowns and unknowns



Do the smae thing for B. BUT DONT USE THE SAME SYMBOLS or you will get confused. (use differetn subscripts). Keep in mind the time it took for train B to reach a velocity is different for the time it took train A to reach that velocity.

Do that first
 
  • #3
this is what I have.

for train A,i'll set the initial velocity as the velocity 5 min before it gets point B,it's 39 m/s

so: Va = 39 + 0.05t

for train B,I assume it starts from rest so:

Vb = at

I can equate them,but as I said before,I only have one equation and 2 unknowns.

I really can't figure this out,I spent like an hour on this problem,but couldn't come up with anything
 
  • #4
thats good

now consider that distance in which they may meet

if A convered a distance d, then what distance has B covered in the same amount of time??
 
  • #5
I'm not following you.
I can't understand how this helps me,with solving the equation.

but the distance is speed*time.

or should I use:
x = x0 + v0t + 0.5at^2
?

thanks for your help
 
  • #6
It is certainly best to set up the similar equations for the POSITIONS, and use those to solve the problem
 
  • #7
but even with the positions,I get 2 unknowns.

I don't know where they meet,and I don't know the acceleration of train B.
 
  • #8
First, you should write down the position functions for each train:
[tex]x_{A}(t)=x_{A,0}+v_{A,0}t+\frac{a_{A}t^{2}}{2}[/tex]
[tex]x_{B}(t)=x_{B,0}+v_{B,0}t+\frac{a_{B}t^{2}}{2}[/tex]

where:
[tex]x_{A,0}=x_{A}(0), x_{B,0}=x_{B}(0), v_{A,0}=v_{A}(0), v_{B,0}=v_{B}(0)[/tex]
Do you agree with this?

Now, you need to define what your spatial and temporal origin should be, before trying to determine the various quantities involved.
 

Related to Help Needed: Solving Train Acceleration Problem

1. What is the train acceleration problem?

The train acceleration problem refers to the difficulty in achieving a desired acceleration or speed in a train, usually due to mechanical or technical issues.

2. What are the common causes of train acceleration problems?

The common causes of train acceleration problems include faulty or worn out locomotives, inadequate power supply, track obstructions, and human error.

3. How do scientists solve train acceleration problems?

Scientists use a combination of mathematical models, computer simulations, and physical tests to identify and address the underlying causes of train acceleration problems. They also work closely with engineers and technicians to implement solutions.

4. What are some potential solutions to train acceleration problems?

Potential solutions to train acceleration problems may include repairing or replacing faulty components, improving power supply systems, adjusting track conditions, and implementing better maintenance and operational procedures.

5. How can train acceleration problems be prevented?

To prevent train acceleration problems, regular maintenance and inspections should be carried out on trains and related equipment. Additionally, implementing advanced monitoring technologies and training personnel on proper procedures can help prevent future issues.

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