Derivative of the kinetic energy

[watsup91749]

Derivative of the kinetic energy...

Homework Statement

If you take the derivative of the kinetic energy of a particle with respect to its velocity you get...
A) force
B) momentum
C) acceleration
D) mass
E) potential energy

Homework Equations

K= .5mv^2

The Attempt at a Solution

Im in pre calc right now and i have no idea how to take the derivative of anything, quick google searching led me to believe that its a calculus thing, so it would be really helpfull if someone could explain how to do this..

 

[rock.freak667]

If you have

$$y=kx^n$$

and you want to find the derivative of that with respect to x,denoted as $\frac{dy}{dx}$

it is simply

$$\frac{dy}{dx}=knx^{n-1}$$Where k is a constant

 

[watsup91749]

I think the answer is B momentum, is that right? momentum has p=mv and kinetic energy has the same variables, so it must be B right?
Also K=mv^(2-1) would be the same as K=mv which is the the same as momentum, is this correct?

 

[rock.freak667]

$$\frac{dK}{dv}=mv$$ which is momentum so you are correct.

 

[awvvu]

You could also exploit the notation and think about it in terms of units.

$$dK/dv = [\frac{kg * m^2/s^2}{m/s}] = [kg * m/s]$$