Relative Speed Trains Formulas

In this class, We discuss Relative Speed Trains Formulas.

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The reader should have prior knowledge of the speed and distance formula. Click Here.

Formula 1:

Time taken by a train of length l meters to pass a pole or a standing man or o signal post is equal to that of a train to pass l meters.

The below diagram shows the graphical understanding of formula 1.

The train has to pass the signal post. I.e. train has to pass the length of the train.

Formula 2:

Time taken by a train of length l meters to pass an object of length b meters is the time taken by the train of the length of l+b meters.

The below diagram shows the graphical intuition of the train and object.

The train has to pass the length of the platform and the length of the train.

Formula 3:

Suppose two trains or objects move in the same direction at u m/s and v m/s, respectively.

Then their relative speed = |u – v| m/s.

First, we need to understand what relative speed is?

Take two objects.

1) Green Object

2) Orange object

Green object speed is two m/s

Orange object speed is five m/s.

After one second, the green object moves 2 meters, and the orange object moves 5 meters.

Relative Speed: At what speed the orange object is moving away from the green object.

The objects are moving away at three m/s.

After two seconds, the green object moves 4 meters, and the orange object moves 10 meters.

The objects are 6 meters away from each other.

The below diagram shows the relative speed.

Relative speed = |5 – 2| m/s.

Formula 4:

Suppose two trains or bodies move in the opposite direction at u m/s and v m/s.

Then their relative speed = u + v m/s.

The below diagram shows the relative speed.

The green and orange objects come close at a speed of 7 m/s.

After one second, the green object moves 2 meters, and the orange object moves 5 meters. So they are coming close at seven m/s.

Relative Speed = 5+2 m/s.

Formula 5:

If two trains of length a and b meters move in the opposite direction at u and v m/s. Then the time taken by the trains to cross each other = (a + b)/(u + v)

Understand the procedure of how we got the formula?

Remembring the formula will not help to solve the bits.

The below diagram shows the process of crossing the trains.

We consider relative speed. Because both objects are moving.

The distance the two objects cover before they cross each other is a + b.

Time = distance / speed

speed = u+v

Time = (a + b)/(u + v)

Formula 6:

If two trains of length a and b meters move in the same direction at u and v m/s. Then the time is taken by faster train to cross the slower train = (a + b)/(u – v)

The below diagram shows the crossing of two trains.

Distance traveled befor cossing = a+b.

Relative speed = u – v

Time to cross = (a + b)/(u – v)