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Motion In Straight Line

Question
CBSEENPH11019914
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On a two-lane road, car A is travelling with a speed of 36 km h-1. Two cars B and C approach car A in opposite directions with a speed of 54 km h-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident ?

Solution
Velocity space of space car space straight A comma space straight v subscript straight A space end subscript equals space 36 space km divided by straight h space equals space 10 space straight m divided by straight s space Velocity space of space car space straight B comma space straight v subscript straight B space equals space 54 space km divided by straight h space equals space 15 space straight m divided by straight s space Velocity space of space car space straight C comma space straight v subscript straight C space equals space 54 space km divided by straight h space equals space 15 space straight m divided by straight s Relative space velocity space of space car space straight B space with space respect space to space car space straight A comma space space straight v subscript BA space equals space straight v subscript straight B space – space straight v subscript straight A space equals space 15 space – space 10 space equals space 5 space straight m divided by straight s space Relative space velocity space of space car space straight C space with space respect space to space car space straight A comma space space straight v subscript CA space end subscript equals space straight v subscript straight C space – space left parenthesis – space straight v subscript straight A right parenthesis space equals space 15 space plus space 10 space equals space 25 space straight m divided by straight s space At space straight a space certain space instance comma space both space cars space straight B space and space straight C space are space at space the space same space distance space from space car space straight A space straight i. straight e. comma space space straight s space equals space 1 space km space equals space 1000 space straight m space space Time space taken space left parenthesis straight t right parenthesis space by space car space straight C space to space cover space 1000 space straight m space equals space 1000 space divided by space 25 space equals space 40 space straight s space Hence comma space to space avoid space an space accident comma space car space straight B space must space cover space the space same space distance space in space straight a space maximum space of space 40 space straight s. space From space second space equation space of space motion comma minimum space acceleration space left parenthesis straight a right parenthesis space produced space by space car space straight B space can space be space obtained space as colon space straight s space equals space ut space plus space left parenthesis 1 divided by 2 right parenthesis at squared space 1000 space space space space equals space 5 space cross times space 40 space plus space left parenthesis 1 divided by 2 right parenthesis space cross times space straight a space cross times space left parenthesis 40 right parenthesis squared space straight a space space space equals space 1600 space divided by space 1600 space equals space 1 space ms to the power of negative 2 end exponent

Some More Questions From Motion in Straight Line Chapter

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

 A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion: 

(a) A kite flying in the sky.

(b) The earth revolving around the sun. 

(c) A train moving along the equator of the earth in clockwise direction. 

(d) Accelerated motion of a particle in a straight line.

Define distance.

Define displacement.

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