When velocity is halved, its kinetic energy becomes 1/4^th .

Question

Write true or false for the following statements: 

When velocity is halved, its kinetic energy becomes 1/4^th.

Answer 1

True 

Explanation: Kinetic energy KE of a body of mass m moving with velocity or speed v is given by the formula: 

KE = \(\frac{1}{2}\) mv² 

so kinetic energy is directly proportional to the mass of object and to the square of speed of the body. 

KE₁ = \(\frac{1}{2}\) mv₁² 

If the velocity of body is halved then kinetic energy 

KE₂ = \(\frac{1}{2}\) mv₂² where, v₂ = \(\frac{1}{2}\) v₁ 

Substituting the value of v₂ in the formula, 

KE₂ =\(\frac{1}{2}\)m (\(\frac{1}{2}\) v₁)² 

= \(\frac{1}{4}\) ( \(\frac{1}{2}\)mv₁² ) 

KE₂ = \(\frac{1}{4}\) KE₁ 

So kinetic energy will become \(\frac{1}{4}\) if the speed is halved.