# If an object with a mass of 5 kg  changes speed from 3m/s to  14m/s, by how much does its kinetic energy change?

Apr 28, 2018

THe change in kinetic energy is $= 467.5 J$

#### Explanation:

The kinetic energy is

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

The change in kinetic energy is

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

The mass is $m = 5 k g$

The initial velocity is ${v}_{1} = 3 m {s}^{-} 1$

The final velocity is ${v}_{2} = 14 m {s}^{-} 1$

Therefore,

$\Delta K E = \frac{1}{2} \times 5 \times \left({14}^{2} - {3}^{2}\right) = 467.5 J$