# Thread: 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:
$\displaystyle \mbox{Kinetic Energy} = \frac{1}{2}mv^2$
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?

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

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

$\displaystyle E_2 = 4E_1$

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

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

$\displaystyle v_2 = 2 v_1$

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# By what factor does the kinetic energy of a particle increased the speed is increased by a factor of of3

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