Question

Calculate the decrease in the kinetic energy of a moving body if it's velocity reduces to one third of the initial velocity

Answer 1

If initial​ kinetic energy of the body is mv²/2 and its velocity decreases to one third.
Therefore the new kinetic energy, is

m(v/3)²/2 =(1/9)mv²/2

the decrease in kinetic energy = mv²/2-(1/9)mv²/2 = (8/9)mv²/2

percentage decrease =
{ {(8/9)mv²/2}/mv²/2}×100
8×100/9 =88.89%

Answer 2

If velocity is reduced to 1/3rd (keeping the mass same),the kinetic energy reduces to 1/9th it's initial value (since kinetic energy is directly proportional to the square of velocity). K1 - K2=K1-1/9K1=8/9th K1(i.e. 8/9th of the initial kinetic energy)