JEE advance 2013 - A particle of mass 0.2 kg

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. The initial speed (in m / s ) of the particle is zero, the speed ( in m / s ) after 5 sec is_ _ _ _ 

{ JEE advance 2013 }

Solution :

Given:

Mass of particle:-           m       =       0.2 kg

Power :-                          P       =       0.5 W

Initial speed :-                u_o      =       0 m / s

Time :-                           t        =       5 sec

Speed of particle :-        v        =       ? m / s

after time ( t )

The kinetic Energy of particle can be given as

        K.E. = ( 1 / 2 ) m v²

i.e. work done is

             w = ( 1 / 2 ) m v²  

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ( 1 )

We know that, the power can be define as wok done per unit time

i.e.

          P = w / t

w = P t

 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ( 2 )

From equation ( 1 ) and ( 2 ) we get,

             P t = ( 1 / 2 ) m v²  

Therefore,

v²  = ( 2 P t ) / m

v = √ [ ( 2 P t ) / m ]

Putting the values of P, t and m in above equation we get,

v = √ [ ( 2 X 0.5 X 5 ) / 0.2 ]

v = √ ( 25 )

v = 5 m / s

The speed of particle after 5 sec is 5 m / s.