Title: **Physics Questions**

Post by:**Medeek** on **May 17, 2019, 01:27:14 PM**

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Has anyone else ever wondered where the 1/2 comes from in the equation for the kinetic energy of an object (E=1/2mv^2)? It finally donned on me why, I probably could have realized why years ago but I never really thought about it until now.

Title: **Re: Physics Questions**

Post by:**Medeek** on **May 17, 2019, 01:29:35 PM**

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The short answer is that it has to do with the integration of the momentum term in the derivation of the kinetic energy.

The more formal answer is:

(http://design.medeek.com/resources/physics/kinectic_energy_pg1.jpg)

(http://design.medeek.com/resources/physics/kinectic_energy_pg2.jpg)

Strangely enough I only thought about this while I was reading on a completely different topic and noticed that the equation given for the potential energy stored in a spring is E = 1/2kx^2. I occurred to me that this expression looked surprisingly similar to the expression for kinetic energy. It all became clear to me when I realized that the momentum is a linear function of the velocity (p=mv) as is the force a linear function of the displacement (F=kx).

The more formal answer is:

(http://design.medeek.com/resources/physics/kinectic_energy_pg1.jpg)

(http://design.medeek.com/resources/physics/kinectic_energy_pg2.jpg)

Strangely enough I only thought about this while I was reading on a completely different topic and noticed that the equation given for the potential energy stored in a spring is E = 1/2kx^2. I occurred to me that this expression looked surprisingly similar to the expression for kinetic energy. It all became clear to me when I realized that the momentum is a linear function of the velocity (p=mv) as is the force a linear function of the displacement (F=kx).