Position of a 3 ~kg mass moving along the X -axis is given by x=0.3 ( t) m . If K(t) denotes the kinetic energy at time t . Then the value of K ( 6 ) K ( 3 ) is

Step-by-step solution

Given, position of particle of mass (m=3 ~kg ) is x=0.3 t Velocity of particle, v= d x d t v= d d t 0.3 t aligned & =0.3 d d t t=0.3(- t) & =-0.3 t aligned Now, at t= 6 , Velocity, v₁=-0.3 ( 6 ) v₁=-0.3 6 = -0.3 2 At t= 3 , Velocity, v₂=-0.3 3 v₂=- -0.3 3 3 Ratio of kinetic energies, aligned & K ( 6 ) K ( 3 ) = 1 2 m v₁^2 1 2 m v₂^2 = ( v₁ v₂ )^2 & K ( 6 ) K ( 3 ) = (- 0.3 2 )^2 (-0.3 3 2 )^2 = 1 3 aligned