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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 car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is:

  • fraction numerator 2 straight v subscript straight d straight v subscript straight u over denominator straight v subscript straight d plus straight v subscript straight u end fraction
  • square root of straight v subscript straight u straight v subscript straight d end root
  • fraction numerator straight v subscript straight d straight v subscript straight d over denominator straight v subscript straight d plus straight v subscript straight u end fraction
  • fraction numerator straight v subscript straight u space plus straight v subscript straight d over denominator 2 end fraction

A.

fraction numerator 2 straight v subscript straight d straight v subscript straight u over denominator straight v subscript straight d plus straight v subscript straight u end fraction

The average speed of a body in a given time interval is defined as the ratio of distance travelled to the time taken.

Average space speed space equals space fraction numerator Distance space travelled over denominator Time space taken end fraction
Let t1 and t2 be times taken by the car to go from X and Y and then Y to X respectively.

Then, 

straight t subscript 1 space plus straight t subscript 2 space equals space XY over straight v subscript straight u space plus XY over straight v subscript straight d space equals space XY space open parentheses fraction numerator straight v subscript straight u space plus straight v subscript straight d over denominator straight v subscript straight u straight v subscript straight d end fraction close parentheses
Total space distance space travelled
equals space XY space plus space XY space equals space 2 XY
Therefore comma space average space speed space of space the space car space for space this space round space trip space is
straight v subscript av space equals space fraction numerator 2 XY over denominator XY open parentheses begin display style fraction numerator straight v subscript straight u plus straight v subscript straight d over denominator straight v subscript straight u straight v subscript straight d end fraction end style close parentheses end fraction
or
straight v subscript av space equals space fraction numerator 2 straight v subscript straight u straight v subscript straight d over denominator straight v subscript straight u plus straight v subscript straight d end fraction

The average speed of a body in a given time interval is defined as the ratio of distance travelled to the time taken.

Average space speed space equals space fraction numerator Distance space travelled over denominator Time space taken end fraction
Let t1 and t2 be times taken by the car to go from X and Y and then Y to X respectively.

Then, 

straight t subscript 1 space plus straight t subscript 2 space equals space XY over straight v subscript straight u space plus XY over straight v subscript straight d space equals space XY space open parentheses fraction numerator straight v subscript straight u space plus straight v subscript straight d over denominator straight v subscript straight u straight v subscript straight d end fraction close parentheses
Total space distance space travelled
equals space XY space plus space XY space equals space 2 XY
Therefore comma space average space speed space of space the space car space for space this space round space trip space is
straight v subscript av space equals space fraction numerator 2 XY over denominator XY open parentheses begin display style fraction numerator straight v subscript straight u plus straight v subscript straight d over denominator straight v subscript straight u straight v subscript straight d end fraction end style close parentheses end fraction
or
straight v subscript av space equals space fraction numerator 2 straight v subscript straight u straight v subscript straight d over denominator straight v subscript straight u plus straight v subscript straight d end fraction

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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

What is a scalar quantity?

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

Force, impulse and momentum.
865 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 Views

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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