A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v= α√x . The displacement of the particle varies with time as from Physics Motion in A Plane Class 11 Manipur Board
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Motion in A Plane

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Physics Part I

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A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v= α√x . The displacement of the particle varies with time as

  • t3

  • t2

  • t

  • t1/2


B.

t2

straight v equals space straight alpha square root of straight x
dx over dt space equals space straight alpha square root of straight x space space space space open parentheses therefore space straight v space equals space dv over dt close parentheses
fraction numerator dx over denominator square root of straight x end fraction space equals space straight alpha space dt
Perform space integration
integral subscript 0 superscript straight x fraction numerator dx over denominator square root of straight x end fraction space equals space integral subscript 0 superscript straight t straight alpha space dt
because space at space straight t space equals space 0 comma space straight x space equals space 0 space and space let space at space any space time space straight t comma space particle space is space at space straight x right square bracket
rightwards double arrow right enclose space fraction numerator straight x to the power of 1 divided by 2 end exponent over denominator 1 divided by 2 end fraction end enclose subscript 0 superscript straight x space equals space αt
rightwards double arrow space straight x to the power of 1 divided by 2 end exponent space equals space straight alpha over 2 straight t
rightwards double arrow space straight x space equals space straight alpha squared over 4 straight x space straight t squared space rightwards double arrow space straight x proportional to space straight t squared
straight v equals space straight alpha square root of straight x
dx over dt space equals space straight alpha square root of straight x space space space space open parentheses therefore space straight v space equals space dv over dt close parentheses
fraction numerator dx over denominator square root of straight x end fraction space equals space straight alpha space dt
Perform space integration
integral subscript 0 superscript straight x fraction numerator dx over denominator square root of straight x end fraction space equals space integral subscript 0 superscript straight t straight alpha space dt
because space at space straight t space equals space 0 comma space straight x space equals space 0 space and space let space at space any space time space straight t comma space particle space is space at space straight x right square bracket
rightwards double arrow right enclose space fraction numerator straight x to the power of 1 divided by 2 end exponent over denominator 1 divided by 2 end fraction end enclose subscript 0 superscript straight x space equals space αt
rightwards double arrow space straight x to the power of 1 divided by 2 end exponent space equals space straight alpha over 2 straight t
rightwards double arrow space straight x space equals space straight alpha squared over 4 straight x space straight t squared space rightwards double arrow space straight x proportional to space straight t squared
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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
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Give three examples of scalar quantities.

Mass, temperature and energy
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Give three examples of vector quantities.

Force, impulse and momentum.
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