What is the derivative of the kinetic energy function?

Question

8859 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-09T08:14:24

It gives us the momentum equation respect to velocity...

The function or equation for kinetic energy is:

$K E = \frac{1}{2} m v^{2}$ $bb(KE)=1/2mv^2$

Taking the derivative respect to velocity $(v)$ $(v)$ we get:

$\frac{d}{d v} (\frac{1}{2} m v^{2})$ $d/(dv)(1/2mv^2)$

Take the constants out to get:

$= \frac{1}{2} m \cdot \frac{d}{d v} (v^{2})$ $=1/2m*d/(dv)(v^2)$

Now use the power rule, which states that $\frac{d}{d x} (x^{n}) = n x^{n - 1}$ $d/dx(x^n)=nx^(n-1)$ to get:

$= \frac{1}{2} m \cdot 2 v$ $=1/2m*2v$

Simplify to get:

$= m v$ $=mv$

If you learn physics, you should clearly see that this is the equation for momentum, and states that:

$p = m v$ $p=mv$