Write true or false for the following statements: When velocity is ha

1.	Write true or false for the following statements: When velocity is halved, its kinetic energy becomes 1/4th.
Answer» 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 = \(\frac{1}{2}\) mv₂²where, v₂ = \(\frac{1}{2}\) v₁ Substituting the value of v₂in 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.

Write true or false for the following statements: When velocity is halved, its kinetic energy becomes 1/4th.

Answer»

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 = \(\frac{1}{2}\) mv₂²where, v₂ = \(\frac{1}{2}\) v₁

Substituting the value of v₂in 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.

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