# Kinetic energy of body is increased by 300 % momentum of body is increased by?

Aug 3, 2018

Momentum increased to double, an increase of 100%.

#### Explanation:

Assume the increase is because of increase in speed (instead of increase in mass -- a bit hard to imagine how that would happen).

If initial KE was $K {E}_{i}$ and KE was increased by 300% it is now

$K {E}_{i} + 3 \cdot K {E}_{i} = 4 \cdot K {E}_{i}$.

The formula for KE is

$K E = \frac{1}{2} \cdot m \cdot {v}^{2}$

Since we assume the only parameter that changed was the velocity, the final velocity is 4 X the initial velocity. Therefore the final velocity is

${v}_{f} = \sqrt{4 \cdot {v}_{i}^{2}} = 2 \cdot {v}_{i}$

Since momentum is m*v,

the original momentum was $m \cdot {v}_{i}$.

Since the final velocity is $2 \cdot {v}_{i}$,

final momentum is $m \cdot 2 \cdot {v}_{i}$

Momentum increased to double, an increase of 100%.

I hope this helps,
Steve