Kinetic energy of the particle is $\"\"$ .

Where $\"\"$ mass of the particle and $\"\"$ speed of the particle.

Case 1:

Initially the partical moves with a speed of $\"\"$ .

Kinetic energy of the particle is $\"\"$

Case 2:

After sometime the partical moves with a speed of $\"\"$ .

Kinetic energy of the particle is $\"\"$ .

The speed of the particle is halved then $\"\"$ .

$\"\"$ .

$\"\"$

Thus kinetic energy changes by a factor of 0.25.

If the speed of a particle is halved, then the kinetic energy of the particle changes by a factor of 0.25.