# An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 96 KJ to  108 KJ over t in [0, 3 s]. What is the average speed of the object?

Feb 8, 2017

5.83 m/s

#### Explanation:

Kinetic energy = $\left(\frac{1}{2}\right) \cdot M \cdot {V}^{2}$ The average speed will be the average of the initial and final velocities.
1 Joule is equivalent to $1 k g \cdot {\left(\frac{m}{s}\right)}^{2.}$
${\left({V}_{1}\right)}^{2} = \left(\frac{96 \cdot 2}{6}\right) \mathmr{and} {\left({V}_{2}\right)}^{2} = \left(\frac{108 \cdot 2}{6}\right)$
${\left({V}_{1}\right)}^{2} = 32 \mathmr{and} {\left({V}_{2}\right)}^{2} = 36$
${V}_{1} = 5.66 \mathmr{and} {V}_{2} = 6$ ;
The average is (5.66 + 6)/2 = 5.83 m/s
The duration of the acceleration is irrelevant.

Mar 10, 2017