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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 particle of unit mass undergoes one-dimensional motion such that its velocity according to
V(x) =  βx-2n where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by 

  • -2nβ2 x-2n-1

  • -2nβx-4n-1

  • -2β x-2n+1

  • -2nβ2e-4n+1


B.

-2nβx-4n-1

Given, v = βx-2n
straight a equals space dv over dt equals dx over dt. dv over dx
straight a equals straight v dv over dx equals left parenthesis space βx to the power of negative 2 straight n end exponent right parenthesis left parenthesis negative 2 straight n space βx to the power of negative 2 straight n minus 1 end exponent right parenthesis
straight a equals negative 2 nβ squared straight x to the power of negative 4 straight n minus 1 end exponent

Given, v = βx-2n
straight a equals space dv over dt equals dx over dt. dv over dx
straight a equals straight v dv over dx equals left parenthesis space βx to the power of negative 2 straight n end exponent right parenthesis left parenthesis negative 2 straight n space βx to the power of negative 2 straight n minus 1 end exponent right parenthesis
straight a equals negative 2 nβ squared straight x to the power of negative 4 straight n minus 1 end exponent

2349 Views

What is a scalar quantity?

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

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. 


814 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