A train of length 200 m travelling at 30 m s^-1 overtakes another train of length 300 m trav

step 1 We will be solving this question by using the concept of relative velocity. So here relative vel

A train of length 200 m travelling at 30 m s^-1 overtakes...

A train of length $200 \mathrm{~m}$ travelling at $30 \mathrm{~m} \mathrm{~s}^{-1}$ overtakes another train of length $300 \mathrm{~m}$ travelling at $20 \mathrm{~m} \mathrm{~s}^{-1}$ in the same direction on a parallel track. The time taken by the first train to cross the second is (a) $30 \mathrm{~s}$ (b) $50 \mathrm{~s}$ (c) $10 \mathrm{~s}$ (d) $20 \mathrm{~s}$

A train of length $200 \mathrm{~m}$ travelling at $30 \mathrm{~m} \mathrm{~s}^{-1}$ overtakes another train of length $300 \mathrm{~m}$ travelling at $20 \mathrm{~m} \mathrm{~s}^{-1}$ in the same direction on a parallel track. The time taken by the first train to cross the second is
(a) $30 \mathrm{~s}$
(b) $50 \mathrm{~s}$
(c) $10 \mathrm{~s}$
(d) $20 \mathrm{~s}$

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Key Concepts

Speed, Distance, and Time Relationship

The basic kinematic equation relating speed, distance, and time is central to solving these types of problems. It states that distance equals speed multiplied by time, and can be rearranged to find any of these variables when the other two are known. This relationship underpins the process of calculating the time required for one moving object to cover a specified distance at a given speed, including the cases involving relative speeds.

Distance in Overtaking Situations

In overtaking problems, the distance that needs to be considered is often the combined length of the two objects involved (such as trains or cars) since the entirety of one must pass the entirety of the other. This ensures that the full overtaking process is accounted for, from the point when the front of the overtaking object aligns with the rear of the object being overtaken until it clears the front.

Relative Velocity

Relative velocity is the speed of one object as observed from another moving object. In problems involving objects moving in the same direction, the relative velocity is calculated as the difference between their speeds. This concept is crucial in determining how quickly one object overtakes or separates from another and simplifies the analysis by reducing the problem to a single effective speed.

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