# Work-Energy Theorem

The work-energy theorem is a very important and useful theorem in physics and here I will show you how we get that specific formula in full understanding.

Energy can help us solve many things however, it is a very abstract concept that we have no clue about. While the change in energy of two objects can be the same as the roll down a ramp and different inclinations, the rate at which the kinetic energy gets converted from potential energy is different and that is what we can start analyzing first.

$dK/dt = d(0.5mv^2)/dt = 2*0.5mv(dv/dt) = mv(dv/dt)$

We let $m$ be a constant as we assume that the object itself is not moving at any high speeds and has negligible relativistic effects. That final solution can also be written as:

$mv(dv/dt) = Fv$

We call this expression power and it is exactly what we have been talking about, the rate at which energy is expended to some object such as a car in order to make it move and do work.

$dK/dt = F(dx/dt)$

We can cancel the $dt's$ from both sides.

$dK = Fdx$

$∫ dK = ∫ Fdx$

$K(2) - K(1) = ∫ Fdx$

And that is the work-energy theorem. It is very important and very useful to use in physics, specifically in areas such as gravitational fields, electric fields, and oscillatory motion.

Note by Raghu Alluri
7 months ago

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