# An object has a mass of 2 kg. The object's kinetic energy uniformly changes from 135 KJ to  36KJ over t in [0, 6 s]. What is the average speed of the object?

Jun 11, 2016

I found $9.2 \frac{m}{s}$

#### Explanation:

We need the speed of the object at each instant so we can use the definition of Kinetic Energy $K = \frac{1}{2} m {v}^{2}$ to find it:
${K}_{i} = \frac{1}{2} m {v}_{i}^{2}$
and
${K}_{f} = \frac{1}{2} m {v}_{f}^{2}$

using our data:
$135 = \frac{1}{2} \cdot 2 {v}_{i}^{2}$
${v}_{i} = 11.6 \frac{m}{s}$

and

$36 = \frac{1}{2} \cdot 2 {v}_{f}^{2}$
${v}_{f} = 6 \frac{m}{s}$

we can now use:
${v}_{f} = {v}_{i} + a t$
and find $a$:
$6 = 11.6 + 6 a$
$a = - 0.9 \frac{m}{s} ^ 2$
we now use:
${v}_{f}^{2} = {v}_{i}^{2} + 2 a s$
to find the distance:
$36 = 135 - 2 \cdot 0.9 \cdot s$
$s = 55 m$
So:
$\text{average speed"="distance"/"time} = \frac{s}{t} = \frac{55}{6} = 9.2 \frac{m}{s}$