Question:

The kinetic energy of a particle is increased by a factor of 4.

By what factor does its speed increase?

Attempt:

$\displaystyle \mbox{Kinetic Energy} = \frac{1}{2}mv^2$

So, the particle is the mass

$\displaystyle 1 = \frac{1}{2}mv^2$

$\displaystyle 1 = \frac{1}{2}(4)v^2$

$\displaystyle 2 = 4 \times v^2$

$\displaystyle \frac{2}{4} = v^2$

$\displaystyle 0.5 = v^2$

$\displaystyle v = \sqrt{0.5}$

$\displaystyle v = 0.707$

Where did I go wrong?I think all the steps are wrong right?