How Do You Calculate Train Velocities When Moving in Opposite Directions?

In summary, two trains A and B with lengths of 125m and 100m respectively are moving in opposite directions on parallel tracks. The velocity of train B is three times that of train A. Using the equation Velocity=Distance/Time, it can be determined that the velocity of train A is 14.1 m/s and the velocity of train B is 42.3 m/s. This is calculated by adding the lengths of both trains (225m) and dividing by the time it takes for them to pass each other (4s). It is important to add the lengths of both trains because each train must travel its own length and the other train's length in order to pass each other.
  • #1
psykatic
43
0

Homework Statement


Two trains A and B, 125m and 100m long respectively are moving in opposite directions on parallel tracks. the velocity of the train B is three times that of train A. The train takes 4s to pass each other, calculate the velocity of each train?

Homework Equations


Velocity=[tex]\frac {Distance}{Time}[/tex]

The Attempt at a Solution


Let the velocity of train A be 'v', hence the velocity of the train B would be '3v'.

The relative velocity of train A w.r.t train B = [tex]v_A- v_B[/tex]
=v-(-3v)=4v

The distance to be covered= 125+100= 225m

Velocity=[tex]\frac{Distance}{Time}[/tex]

Hence, velocity, 4v= [tex]\frac{225}{4}[/tex]
Therefore, 16v=225

Thus, v=14.1

Hence, [tex] v_A[/tex]=14.1 m/s and [tex] v_B[/tex]= 42.3 m/sI've reached the final answer, by using the textual methodology. But the thing which is bothering me is the distance covered, which is given by the addition of the length of both the trains (statement highlighted). Please explain me as to why do we add these lenghts, when the entire train (considering it as a whole, either A or B) moves across the length of the other, and not its own!
 
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  • #2
Get two trains and try it...

The moment before they start passing each other:

Train 1 ------------------ Train 2 (total distance = sum of distances)
_______________/////////////////////////
////////////////////// ________________

The moment after they have passed each other:

Train2 ------------------ Train 1

//////////////////////// __________________
________________////////////////////////////


Notice (look at the tails) that each train has to travel its own length, and the other trains length. Hope this helps :)
 
  • #3
oh, yes! got it! actually i was considering one train, and observing it going past the others!
 

Related to How Do You Calculate Train Velocities When Moving in Opposite Directions?

1. What is Basic Relative Velocity Query?

Basic Relative Velocity Query is a scientific method used to calculate the relative velocity between two objects. It takes into account the movement of one object with respect to the other, and calculates the velocity of one object as observed by the other.

2. How is Basic Relative Velocity Query calculated?

The calculation of Basic Relative Velocity Query involves using the velocity of each object and the angle between their directions of movement. This can be represented mathematically as vAB = vA + vB*cos(theta), where vAB is the relative velocity, vA and vB are the velocities of the two objects, and theta is the angle between their directions of movement.

3. What is the importance of Basic Relative Velocity Query?

Basic Relative Velocity Query is important in many scientific fields, including physics, astronomy, and engineering. It helps us understand the movement of objects in relation to each other, and can be used to predict and analyze the behavior of complex systems.

4. Can Basic Relative Velocity Query be used for objects moving in different dimensions?

Yes, Basic Relative Velocity Query can be used for objects moving in different dimensions, as long as the velocities and angle between their directions of movement are known. The calculation may be more complex in this case, but the basic principles still apply.

5. Are there any limitations to Basic Relative Velocity Query?

Basic Relative Velocity Query is a simplified method and may not accurately represent the true relative velocity between two objects in certain situations. It assumes constant velocity and does not take into account factors such as acceleration or gravitational pull. It is important to use more advanced methods when dealing with complex systems.

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