Physics

Physics

Problem

Two trains, A and B, start simultaneously from the opposite ends of a straight track that is 50 km50\,\text{km} long and move towards each other on parallel lines. • Train A travels at a uniform speed of 36 km h−136\,\text{km}\,\text{h}^{-1}. • Train B travels at a uniform speed of 54 km h−154\,\text{km}\,\text{h}^{-1}. Use this information to answer the following: a. (i) Calculate the time after the start at which the two trains meet. b. (ii) Find the distance of the meeting point from the starting point of train A. c. (iii) After crossing, both trains continue with their respective speeds. Determine the additional time taken by train B to reach the station from which train A had started.
Intuitive explanation

When two objects move toward each other, their speeds add to determine how fast the gap between them closes—this is the key to relative motion. Instead of tracking each train separately, think of the problem from one train's perspective: the other train approaches at the sum of both speeds. Once you know the combined closing speed, you can find when they meet by dividing the total distance by that rate.

Intuitive explanation

When two objects move toward each other, their speeds add to determine how fast the gap between them closes—this is the key to relative motion. Instead of tracking each train separately, think of the problem from one train's perspective: the other train approaches at the sum of both speeds. Once you know the combined closing speed, you can find when they meet by dividing the total distance by that rate.

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