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Motion In Straight Line

Question
CBSEENPH11020462
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A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

  • x2

  • ex

  • x

  • logex

Solution

A.

x2

In this problem acceleration (a) is given in terms of displacement (x)  to determine the velocity with respect to position or displacement we have to apply integration method.
From given information a =-kx, where a is acceleration, x is displacement and k is proportionality constant. 
vdx over dx space equals space minus space kx space open square brackets therefore space dv over dt space equals space fraction numerator begin display style dv end style over denominator dx end fraction open parentheses dx over dt close parentheses space equals space straight v dv over dx close square brackets straight v space dv space equals space minus kx space dx
Let for any displacement from 0 to x , the velocity changes from vo to v
integral subscript straight v subscript straight o end subscript superscript straight v space vdv space equals space minus integral subscript 0 superscript straight x space kx space dx rightwards double arrow space integral subscript 0 superscript straight x space kx space dx rightwards double arrow space fraction numerator straight v squared minus straight v subscript 0 superscript 2 over denominator 2 end fraction space equals space minus space kx squared over 2 rightwards double arrow space straight m space open parentheses fraction numerator straight v squared minus space straight v subscript 0 superscript 2 over denominator 2 end fraction close parentheses space equals space fraction numerator negative mkx squared over denominator 2 end fraction increment straight K space proportional to space straight x squared

Some More Questions From Motion in Straight Line Chapter

Is absolute rest or absolute motion possible?

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

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.

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