# An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 88 kJ to  48 kJ over t in [0, 6 s]. What is the average speed of the object?

Mar 23, 2016

From the kinetic energy and the mass given, the initial speed is $5.4$ $m {s}^{-} 1$ and the final speed is $4$ $m {s}^{-} 1$. The average speed is $4.7$ $m {s}^{-} 1$.

#### Explanation:

I don't think we actually need to know the time taken. Let's find out.

We know ${E}_{k} = \frac{1}{2} m {v}^{2}$, which we can rearrange to give:

$v = \sqrt{2 {E}_{k} / m}$

That means the initial speed (we don't care about direction) is:

$v = \sqrt{2 {E}_{k} / m} = \sqrt{2 \times \frac{88}{6}} \approx 5.4$ $m {s}^{-} 1$

The final speed is:

$v = \sqrt{2 {E}_{k} / m} = \sqrt{2 \times \frac{48}{6}} = 4$ $m {s}^{-} 1$

Since the object is decelerating uniformly, the average speed will just be:

$\frac{{v}_{\text{initial"+v_"final}}}{2} = \frac{5.4 + 4}{2} = 4.7$ $m {s}^{-} 1$

Whether it decelerated over 1, 2 or 6 seconds, the average speed would be the same.