How is the kinetic energy of a moving cart affected if (a) its mass is doubled, (b)its velocity is reduced to (1)/(3)rd of the initial velocity ?

How is the kinetic energy of a moving cart affected if (a) its mass is

1.	How is the kinetic energy of a moving cart affected if (a) its mass is doubled, (b)its velocity is reduced to (1)/(3)rd of the initial velocity ?
Answer» Solution :(a)`K_(1)=(1)/(2)mv^(2).K_(2)=(1)/(2)xx2mxxv^(2)` `therefore K_(2)=2K_(1)` Alternative :If mass m is doubled (keeping the SPEED same),the kinetic energy gets doubled (since kinetic energy is directly proportional to the mass) i.e., Increase in kinetic energy =`K_(2)-K_(1)=2K_(1)-K_(1)` `=K_(1)` (initial kinetic energy ) (b)`K_(1)=(1)/(2)mv^(2),k_(2)=(1)/(2)mxx((1)/(3)v)^(2)=(1)/(9)xx(1)/(2)mv^(2)` `therefore K_(2)=(1)/(9)K_(1)` ALternative :If VELOCITY v is reduced to `(1)/(3)`rd (keeping the mass same),the kinetic energy reduces to `(1)/(9)TH` initial value (since kinetic energy is directly proportional to the square of velocity). i.e. Decreases in kinetic energy =`K_(1)-K_(2)=K_(1)-(1)/(9)K_(1)` `=(8)/(9)K_(1)` (i.e. `(8)/(9)th` the initial kinetic energy )