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Question 1: If you are riding on a train that speeds past another train moving in the same direction on an adjacent track, it appears that the other train is moving backward. Why?

Answer

We cannot understand the problem unless we know about two things; relative velocity and frame of reference.
Relative velocity: A person is standing on the bank of road and a car passes with a velocity of 100 km/hr. Another car is following the first car with the same speed, 100 km/hr. If you were sitting in second car and noting at what velocity does the first car moves away from you. Surely, zero. Because the displacement of your car does not change with respect to the car in front of you (velocity = displacement/time). Thus we say the velocity of car 1 is zero relative to car 2 (though it is 100 km/hr with respect to the person on the road). Now think about various situation when the velocities of the car are different from one another. Relative velocity is calculated by subtracting the one VELOCITY VECTOR from the other VELOCITY VECTOR.
Frame of reference: Without going into the details of definition of frame of reference, in this case we say a frame of reference is a region of space (and surely, the objects within it) moving with the same velocity. The train is your frame of reference in this problem. The car is the frame of reference in the above example.

The two trains are moving on two adjacent (nearby) tracks. The train we sit in is moving fast than the other train.

The two trains together constitute a system of two frames of reference moving away from one another with some relative velocity. The relative velocity of the trains will be equal to the difference of the two velocity vectors of the trains.

We will not be experiencing the velocity of our frame of reference (our train) because everything in our train is moving with the same velocity. However, when we look at the other train, we will observe it is moving with the relative velocity of the two trains (or frames of reference). This relative velocity of the other train as seen from ours, will be equal to the velocity of that train minus the velocity of our train. When we subtract it as vectors, we find the velocity of the other train is back to our front. Thus we will observe the train is moving backwards.

When we are traveling in a bus, the trees of the bank of road seems running backwards. Do you know why it is so?

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  1. Pingback:Conceptual Questions Forces and Motion, Physics 11 – msa

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