Question

what changes take place in kinetic energy if velocity becomes half and double​

Answer 1

Answer:

(i) Kinetic energy becomes one-fourth if velocity becomes half

(ii) Kinetic energy becomes four times if velocity becomes double

Explanation:

• Kinetic Energy of an object is the energy possessed by it by virtue of its motion.

The Kinetic Energy of an object is given by,

  $\underline{\boxed{\bf KE=\dfrac{1}{2}mv^2}}$

where

❖ m denotes mass of the object

❖ v denotes velocity of the object.

 So, Kinetic energy is directly proportional to square of the velocity.

Case - (i) : if velocity becomes half

 Let v' = v/2

Then kinetic energy becomes, ( let it be KE' )

 $\sf KE'=\dfrac{1}{2}mv'^2 \\\\ \sf KE'=\dfrac{1}{2}m\bigg(\dfrac{v}{2}\bigg)^2 \\\\ \sf KE'=\dfrac{1}{2}m \times \dfrac{v^2}{4} \\\\ \sf KE'=\dfrac{1}{4}KE$

Therefore, if velocity of the object becomes half, then kinetic energy becomes one fourth of the initial kinetic energy.

Case - (ii) : if velocity becomes double

 Let v'' = 2v

The Kinetic energy becomes, ( let it be KE'' )

 $\sf KE''=\dfrac{1}{2}mv''^2 \\\\ \sf KE''=\dfrac{1}{2}m(2v)^2 \\\\ \sf KE''=\dfrac{1}{2}m \times 4v^2 \\\\ \sf KE''=4KE$

Therefore, if velocity of the object becomes double, then kinetic energy becomes four times the initial kinetic energy.