# If an object with a mass of 2 kg  changes speed from 2 m/s to  4m/s, by how much does its kinetic energy change?

Jun 14, 2018

$12$ Joules

#### Explanation:

Given: mass $= 2 k g$, changes speed from $2 \frac{m}{s} \text{ to } 4 \frac{m}{s}$. Find the $\Delta K E$

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

$\Delta K E = \frac{1}{2} m {v}_{2}^{2} - \frac{1}{2} m {v}_{1}^{2}$

$\Delta K E = \frac{1}{2} \left(2\right) {4}^{2} - \frac{1}{2} \left(2\right) {2}^{2}$

The units $1 \left(k g \cdot {m}^{2} / {s}^{2}\right) = 1$ Joule

$\Delta K E = 16 - 4 = 12$ Joules

Since the mass stays the same you could have simplified the equation by factoring:

$\Delta K E = \frac{1}{2} m \left({v}_{2}^{2} - {v}_{1}^{2}\right)$

$\Delta K E = \frac{1}{2} \left(2\right) \left({4}^{2} - {2}^{2}\right)$

$\Delta K E = 16 - 4 = 12$ Joules