Question

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

Answer 1

Answer: by a factor of √2

Explanation:

The kinetic energy is written as:

K = (m/2)*v^2

where m is the mass of the particle and v is the velocity:

If we double the kinetic energy, we have:

k' = 2k = 2(m/2)*v^2

now we want to see by what factor is increased the velocity, so we must put that 2 inside the square power, this is:

k' = 2*(m/2)*(v)^2 = (m/2)*(√2*v)^2 is the new kinetic energy,

This means that the velocity is increased by a factor of √2

Answer 2

 velocity increases by √3