Answer: by a factor of √2
Step-by-step 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