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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 moves a distance x in time t according to equation x  = (t +5)-1. The acceleration of particle is proportional to

  • (velocity)3/2

  • (distance)2

  • (distance)-2

  • (velocity)2/3


A.

(velocity)3/2

Given, distance x = ( t + 5)-1   ...... (i)

Differentiating eq. (i) w.r.t, we get

dx over dt space equals space straight v space equals space fraction numerator negative 1 over denominator left parenthesis straight t plus 5 right parenthesis squared end fraction space space space space.... space left parenthesis ii right parenthesis

Again space comma space differentiating space eq space left parenthesis straight i right parenthesis thin space straight w. straight r. straight t comma space we space get
fraction numerator straight d squared straight x over denominator dt squared end fraction space equals space left parenthesis straight a right parenthesis space equals space fraction numerator 2 over denominator left parenthesis straight t space plus 5 right parenthesis cubed end fraction
Comparing space eqs. space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis comma space we space get
left parenthesis straight a right parenthesis space proportional to space left parenthesis straight v right parenthesis to the power of 3 divided by 2 end exponent 

Given, distance x = ( t + 5)-1   ...... (i)

Differentiating eq. (i) w.r.t, we get

dx over dt space equals space straight v space equals space fraction numerator negative 1 over denominator left parenthesis straight t plus 5 right parenthesis squared end fraction space space space space.... space left parenthesis ii right parenthesis

Again space comma space differentiating space eq space left parenthesis straight i right parenthesis thin space straight w. straight r. straight t comma space we space get
fraction numerator straight d squared straight x over denominator dt squared end fraction space equals space left parenthesis straight a right parenthesis space equals space fraction numerator 2 over denominator left parenthesis straight t space plus 5 right parenthesis cubed end fraction
Comparing space eqs. space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis comma space we space get
left parenthesis straight a right parenthesis space proportional to space left parenthesis straight v right parenthesis to the power of 3 divided by 2 end exponent 

591 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.
865 Views

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