Two trains A and B each of length 400 m are moving on two parallel tracks with a uniform speed

step 1 In this question we will learn about some basic concepts of equation of motion. So in the given

Two trains A and B each of length 400 m are moving on two...

Two trains $A$ and $B$ each of length $400 \mathrm{~m}$ are moving on two parallel tracks with a uniform speed $72 \mathrm{~km} \mathrm{~h}^{-1}$ in the same direction with $A$ ahead of $B$. The driver of $B$ decides to overtake $A$ and accelerates by $1 \mathrm{~m} \mathrm{~s}^{-2}$. If after $50 \mathrm{~s}$, the guard of $B$ just brushes past $A$, what was the original distance between them? (a) $750 \mathrm{~m}$ (b) $1000 \mathrm{~m}$ (c) $1250 \mathrm{~m}$ (d) $2250 \mathrm{~m}$

Two trains $A$ and $B$ each of length $400 \mathrm{~m}$ are moving on two parallel tracks with a uniform speed $72 \mathrm{~km} \mathrm{~h}^{-1}$ in the same direction with $A$ ahead of $B$. The driver of $B$ decides to overtake $A$ and accelerates by $1 \mathrm{~m} \mathrm{~s}^{-2}$. If after $50 \mathrm{~s}$, the guard of $B$ just brushes past $A$, what was the original distance between them?
(a) $750 \mathrm{~m}$
(b) $1000 \mathrm{~m}$
(c) $1250 \mathrm{~m}$
(d) $2250 \mathrm{~m}$

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Key Concepts

Relative Motion

This concept deals with analyzing the movement of one object as observed from another moving object. In the context of overtaking, it involves calculating the relative speed between the two trains and determining the effective distance that needs to be covered by one train to pass the other.

Uniform Acceleration

Uniform acceleration refers to motion in which the acceleration remains constant over time. The kinematic equations associated with uniform acceleration are used to determine the displacement, velocity, and time, which are key to analyzing how quickly a train can increase its speed during the overtaking maneuver.

Kinematic Equations

Kinematic equations provide the mathematical framework to relate displacement, initial velocity, acceleration, and time. They are instrumental in solving problems involving objects in motion, particularly when one object is accelerating, such as during the overtaking process.

Overtaking Dynamics

This concept encompasses the conditions and calculations involved when one moving object passes another. It requires understanding the measurements of length, initial separation, speeds, and acceleration, as well as the application of relative motion principles and kinematic equations to determine the exact point or time at which overtaking is completed.

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