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Motion in A Plane

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

A body of mass m accelerates uniformly from rest to v1 in time t1. The instantaneous power delivered to the body as a function of time t is

  • fraction numerator mv subscript 1 straight t over denominator straight t subscript 1 end fraction
  • fraction numerator mv subscript 1 superscript 2 space straight t over denominator straight t subscript 1 superscript 2 end fraction
  • fraction numerator mv subscript 1 straight t squared over denominator straight t subscript 1 end fraction
  • fraction numerator mv subscript 1 superscript 2 straight t over denominator straight t subscript 1 end fraction

B.

fraction numerator mv subscript 1 superscript 2 space straight t over denominator straight t subscript 1 superscript 2 end fraction

Let the constant acceleration of body of mass m is a.
From equation of motion

v1 = 0 + at1
⇒ a = t2/t= ...... (i)
At an instant t, the velocity v of the body v = 0 + at

straight v space equals space straight v subscript 1 over straight t subscript 1 straight t space space.... space left parenthesis ii right parenthesis
therefore space instantaneous space power
straight p space equals Fv
space equals mav space space left parenthesis because space straight F space equals space ma right parenthesis
equals space straight m open parentheses straight v subscript 1 over straight t subscript 1 close parentheses space straight x open parentheses straight v subscript 1 over straight t subscript 1 space straight x space straight t close parentheses space left square bracket space From space equ space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
space equals space fraction numerator mv subscript 1 superscript 2 straight t over denominator straight t subscript 1 superscript 2 end fraction

Let the constant acceleration of body of mass m is a.
From equation of motion

v1 = 0 + at1
⇒ a = t2/t= ...... (i)
At an instant t, the velocity v of the body v = 0 + at

straight v space equals space straight v subscript 1 over straight t subscript 1 straight t space space.... space left parenthesis ii right parenthesis
therefore space instantaneous space power
straight p space equals Fv
space equals mav space space left parenthesis because space straight F space equals space ma right parenthesis
equals space straight m open parentheses straight v subscript 1 over straight t subscript 1 close parentheses space straight x open parentheses straight v subscript 1 over straight t subscript 1 space straight x space straight t close parentheses space left square bracket space From space equ space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
space equals space fraction numerator mv subscript 1 superscript 2 straight t over denominator straight t subscript 1 superscript 2 end fraction

515 Views

What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
835 Views

Give three examples of vector quantities.

Force, impulse and momentum.
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Give three examples of scalar quantities.

Mass, temperature and energy
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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. 


814 Views

What is a scalar quantity?

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