# Math Help - By what factor does its speed increase?

1. ## By what factor does its speed increase?

Question:
The kinetic energy of a particle is increased by a factor of 4.
By what factor does its speed increase?

Attempt:
$\mbox{Kinetic Energy} = \frac{1}{2}mv^2$
So, the particle is the mass

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

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

$2 = 4 \times v^2$

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

$0.5 = v^2$

$v = \sqrt{0.5}$
$v = 0.707$

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

2. $E_1 = \frac{1}{2}m (v_1)^2$

$E_2 = \frac{1}{2}m (v_2)^2$

$E_2 = 4E_1$

$\frac{1}{2}m (v_2)^2 = 4\frac{1}{2}m (v_1)^2$

$(v_2)^2 = 4 (v_1)^2$

$v_2 = 2 v_1$