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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 mass m is at rest at the origin at time t = 0. It is subjected to a force F (t) = F0e–bt in the x direction. Its speed v(t) is depicted by which of the following curves?


C.

straight F equals space straight F subscript 0 straight e to the power of negative bt end exponent
rightwards double arrow space straight a space equals space straight F over straight m space equals space straight F subscript 0 over straight m straight e to the power of negative bt end exponent
rightwards double arrow space dv over dt space equals straight F subscript 0 over straight m straight e to the power of negative bt end exponent
integral dv space equals space integral subscript 0 superscript straight t straight F over straight m straight e to the power of negative bt end exponent dt
rightwards double arrow space straight v space equals straight F over straight m open square brackets table row cell negative 1 end cell row straight b end table close square brackets open square brackets table row cell straight e to the power of negative bt end exponent end cell end table close square brackets subscript 0 superscript straight t
rightwards double arrow space straight v equals space straight F over mb left square bracket straight e to the power of negative bt end exponent right square bracket
straight v equals space 0 space at space straight t equals space 0
and space straight v rightwards arrow space straight F over mb space as space straight t rightwards arrow infinity

So, velocity increases continuously and attains a maximum value of v= F/mb as t ∞
straight F equals space straight F subscript 0 straight e to the power of negative bt end exponent
rightwards double arrow space straight a space equals space straight F over straight m space equals space straight F subscript 0 over straight m straight e to the power of negative bt end exponent
rightwards double arrow space dv over dt space equals straight F subscript 0 over straight m straight e to the power of negative bt end exponent
integral dv space equals space integral subscript 0 superscript straight t straight F over straight m straight e to the power of negative bt end exponent dt
rightwards double arrow space straight v space equals straight F over straight m open square brackets table row cell negative 1 end cell row straight b end table close square brackets open square brackets table row cell straight e to the power of negative bt end exponent end cell end table close square brackets subscript 0 superscript straight t
rightwards double arrow space straight v equals space straight F over mb left square bracket straight e to the power of negative bt end exponent right square bracket
straight v equals space 0 space at space straight t equals space 0
and space straight v rightwards arrow space straight F over mb space as space straight t rightwards arrow infinity

So, velocity increases continuously and attains a maximum value of v= F/mb as t ∞
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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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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 scalar quantities.

Mass, temperature and energy
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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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