# An object has a mass of 5 kg. The object's kinetic energy uniformly changes from 150 KJ to  42KJ over t in [0,8s]. What is the average speed of the object?

Nov 12, 2016

The average speed is $= 142.5 m {s}^{- 1}$

#### Explanation:

The kinetic energy $= \frac{m {v}^{2}}{2}$
Let ${u}_{0}$ be the initial velocity and
${u}_{1}$ the final velocity.
The average speed is $= \frac{{u}_{0} + {u}_{1}}{2}$

$m \cdot {u}_{0}^{2} / 2 = 150 \cdot {10}^{3}$
$\therefore {u}_{0}^{2} = 150 \cdot {10}^{3} / 5$ $\implies$${u}_{0} = \sqrt{30 \cdot {10}^{3}} = 173.2 m {s}^{- 1}$

$m \cdot {u}_{1}^{2} / 2 = 42 \cdot {10}^{3}$
$\therefore {u}_{1}^{2} = 42 \cdot {10}^{3} / 5$ $\implies$${u}_{1} = \sqrt{42 \cdot 200} = 91.7 m {s}^{- 1}$

The average speed is $\frac{173.2 + 91.7}{2} = 142.5 m {s}^{- 1}$