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What is the derivative of the kinetic energy function?

Answer 1

William Abdalla

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

The function or equation for kinetic energy is:

#bb(KE)=1/2mv^2#

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

#d/(dv)(1/2mv^2)#

Take the constants out to get:

#=1/2m*d/(dv)(v^2)#

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

#=1/2m*2v#

Simplify to get:

#=mv#

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

#p=mv#

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Answer 2

Luke Alvarez

The derivative of the kinetic energy function with respect to time is equal to the power, which is the rate at which work is done on an object or the rate at which energy is transferred or transformed. Mathematically, it is expressed as the product of the mass of the object and the acceleration of the object in the direction of motion: ( P = \frac{d}{dt} \left(\frac{1}{2}mv^2\right) = m \cdot \frac{dv}{dt} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.