Physics Homework Help?

Question

If the kinetic energy of a particle is doubled, by what factor has its speed increased?

 

I got this answer and it was 1.4 or the squareroot of 2

 

I can not seem to get the second part which is, 

 

If the speed of a particle is halved, by what factor does its kinetic energy change?

 

Above is the answer that I need. 

 

Thank you.

Answer 1

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 .

If 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.