# What is the kinetic energy of an object with a mass of 5  kg that has been in freefall for 12 s?

Mar 13, 2016

There are two possible approaches, one of which involves finding the velocity and the other the distance traveled. Both yield the answer ${E}_{k} = 34 , 574$ $J$.

#### Explanation:

There are a couple of possible approaches, and I'll briefly outline both, just for fun. The first is probably the most popular.

First approach

Find the velocity of the object. We assume no air resistance and an initial velocity of $0$:

$v = u + a t = 0 + 9.8 \cdot 12 = 117.6$ $m {s}^{-} 1$

Now calculate the kinetic energy:

${E}_{k} = \frac{1}{2} m {v}^{2} = \frac{1}{2} \cdot 5 \cdot {117.6}^{2} = 34 , 574$ $J$

Second approach

Find the distance fallen:

$d = u t + \frac{1}{2} a {t}^{2} = 0 \cdot 12 + \frac{1}{2} \cdot 9.8 \cdot {12}^{2} = 705.6$ $m$

Then note that the change in gravitational potential energy will have been converted into kinetic energy. The change in gravitational potential energy will be:

$\Delta {E}_{p} = m g \Delta h = 5 \cdot 9.8 \cdot 705.6 = 34 , 574$ $J$

It's always very reassuring to do the same question two different ways and get the same answer: which is one good reason to learn more than one way to do it!