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Motion in A Plane

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Physics Part I

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Physics

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A body of mass 1 kg begins to move under the action of a time dependent force F = left parenthesis 2 straight t space straight i with hat on top space plus space 3 straight t squared space straight j with hat on top right parenthesis N, where straight i with hat on top space a n d space j with hat on top are units vectors along X and Y axis. What power will be developed by the force at the time (t)?

  • (2t2 + 4t4) W

  • (2t3 + 3 t4) W

  • (2t3 + 3t5) W

  • (2t + 3t3)W


C.

(2t3 + 3t5) W

A body of mass 1 kg begins to move under the action of time dependent force,
F = (2t straight i with hat on top+3t2 straight j with hat on top) N,
where stack straight i space with hat on top a n d space j with hat on top are unit vectors along X and Y axis.
F = ma
rightwards double arrow space straight a space equals space straight F over straight m
rightwards double arrow space straight a space equals space fraction numerator left parenthesis 2 straight t space straight i with hat on top space plus space 3 straight t squared space straight j with hat on top right parenthesis over denominator 1 end fraction space space left square bracket space straight m space equals 1 space kg right square bracket
rightwards double arrow space straight a space equals space left parenthesis 2 straight t space straight i with hat on top space plus space 3 straight t squared space straight j with hat on top right parenthesis space straight m divided by straight s squared

Acceleration, a = dv over dt
rightwards double arrow space dv space equals space straight a. space dt space space space space space space... space left parenthesis straight i right parenthesis
Integrating both sides, we get

integral d v space equals space integral a. space d t
space space space space space space space space space equals space integral left parenthesis 2 t space i with hat on top space plus space 3 t squared space j with hat on top right parenthesis space d t
v space equals space t squared space space i with hat on top space plus straight t cubed space straight j with hat on top
Power developed by the force at the time t will be given as,

P = F.v = (2t straight i with hat on top + 3t2 straight j with hat on top).(straight t squared space straight i with hat on top space plus space straight t cubed space straight j with hat on top)
   = (2t. t2 + 3t2.t3)

P = (2t3 + 3t5) W

A body of mass 1 kg begins to move under the action of time dependent force,
F = (2t straight i with hat on top+3t2 straight j with hat on top) N,
where stack straight i space with hat on top a n d space j with hat on top are unit vectors along X and Y axis.
F = ma
rightwards double arrow space straight a space equals space straight F over straight m
rightwards double arrow space straight a space equals space fraction numerator left parenthesis 2 straight t space straight i with hat on top space plus space 3 straight t squared space straight j with hat on top right parenthesis over denominator 1 end fraction space space left square bracket space straight m space equals 1 space kg right square bracket
rightwards double arrow space straight a space equals space left parenthesis 2 straight t space straight i with hat on top space plus space 3 straight t squared space straight j with hat on top right parenthesis space straight m divided by straight s squared

Acceleration, a = dv over dt
rightwards double arrow space dv space equals space straight a. space dt space space space space space space... space left parenthesis straight i right parenthesis
Integrating both sides, we get

integral d v space equals space integral a. space d t
space space space space space space space space space equals space integral left parenthesis 2 t space i with hat on top space plus space 3 t squared space j with hat on top right parenthesis space d t
v space equals space t squared space space i with hat on top space plus straight t cubed space straight j with hat on top
Power developed by the force at the time t will be given as,

P = F.v = (2t straight i with hat on top + 3t2 straight j with hat on top).(straight t squared space straight i with hat on top space plus space straight t cubed space straight j with hat on top)
   = (2t. t2 + 3t2.t3)

P = (2t3 + 3t5) W

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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.
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Give three examples of vector quantities.

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

Mass, temperature and energy
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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.
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