Motion in Straight Line

Physics Part I

Physics

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Two towns A and B are connected by a regular bus service with a bus leaving inÂ either direction every T minutes. A man cycling with a speed of 20 km h^{-1}Â in theÂ direction A to B notices that a bus goes past him every 18 min in the direction ofÂ his motion, and every 6 min in the opposite direction. What is the period T of theÂ bus service and with what speed (assumed constant) do the buses ply on theÂ road?

LetÂ *V*Â be the speed of the bus running between towns A and B.

Given,Â

Speed of the cyclist Â = 20 km/hrÂ

Relative speed of bus moving in the direction of the cyclist = V - v = (V-20) km/hr

Every 18 mins, the bus went past the cyclist. moving in the direction of the bus.Â

That is,Â

Distance covered by the bus =Â

One bus leaves every t minutes.Â

Therefore,Â

Distance travelled by the bus = VÂ Â Â Â ... (ii)Â

Equations (i) and (ii) are equal.Â

Relative speed of the bus moving in the opposite direction of the cyclistÂ = (*V*Â + 20) km/h

Time taken by the bus to go past the cyclist = 6 min = 6 / 60 hÂ

Therefore,Â

Now, from equations (3) and (4), we get

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What is motion?

When an object changes it's position with time, with respect to it's surroundings, the object is said to be in motion.

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What is the most essential thing to study the motion of a body?

The most essential thing to study the motion is reference frame. Rest and motion are relative terms. It means that an object in one situation can be in rest but in another situation, the same object will be in motion.

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Can a body be always at rest in some frame?

Yes, a body is always at rest in a frame which is fixed with the body itself.

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What is rest?

When an object does not change its position with time, with respect to it's surroundings. In such a case the object is said to be at rest.

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