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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12
The position of a particle is given by
bold r bold space bold equals bold space 3.0 space straight t space straight i with hat on top space minus space 2.0 space straight t squared space straight j with hat on top space plus space 4.0 space straight k with hat on top space straight m
where t is in seconds and the coefficients have the proper units for r to be in metres.

(a) Find the v and a of the particle? 

straight a right parenthesis thin space
straight v with rightwards harpoon with barb upwards on top left parenthesis straight t right parenthesis space equals space left parenthesis 3.0 space straight i with hat on top space minus space 4.0 straight t space straight j with hat on top right parenthesis

straight a space equals space minus 4.0 space straight j with hat on top space

Position space of space the space particle space is space given space by comma space

bold r bold space bold equals bold space 3.0 space straight t space straight i with hat on top space minus space 2.0 space straight t squared space straight j with hat on top space plus space 4.0 space straight k with hat on top space straight m

Velocity comma space straight v with rightwards harpoon with barb upwards on top equals fraction numerator straight d straight r with rightwards harpoon with barb upwards on top over denominator dt end fraction equals straight d over dt left parenthesis bold space 3.0 space straight t space straight i with hat on top space minus space 2.0 space straight t squared space straight j with hat on top space plus space 4.0 space straight k with hat on top space right parenthesis

therefore space straight v with rightwards harpoon with barb upwards on top space equals space 3.0 space straight i with hat on top minus space 4.0 straight t space space straight j with hat on top

Acceleration space of space the space particle space is space given space by comma

straight a with bar on top space equals space fraction numerator straight d straight v with rightwards harpoon with barb upwards on top over denominator dt end fraction space equals space straight d over dt open parentheses space 3.0 space straight i with hat on top minus space 4.0 straight t space space straight j with hat on top close parentheses space

straight a with bar on top space equals space minus space 4.0 space space straight j with hat on top space
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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.
1212 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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Give three examples of scalar quantities.

Mass, temperature and energy
769 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views

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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