# Deriving Formula of Kinetic Energy using f = ma

• Hoddie54
In summary, the conversation discusses deriving the kinetic energy of something moving according to classical mechanics. The equations used are Energy = Force * Displacement and Force = Mass * Acceleration. The individual attempts to solve the problem by substituting 'MA' into the energy equation and rewriting the acceleration as Δv/Δt. The final formula obtained is E = (M * V^2)/2, with a potential error in the integral ∫(M * V * Δv).
Hoddie54

## Homework Statement

I am not fully sure where this is supposed to go, so forgive me if I get it wrong. I am just undertaking some private research and want to see if my work is correct. I wish to derive the Kinetic energy of something moving according to classical mechanics.

## Homework Equations

Energy = Force * Displacement (Or distance moved).
Force = Mass * Acceleration

## The Attempt at a Solution

Firstly I substituted 'MA' into Energy = Mass * Acceleration * Displacement.
Acceleration can be rewritten as Δv/Δt, and so I change my formula to be Energy = M * Δv/Δt * displacement. To find the Energy, in respect to the displacement we can make the integral ∫(M * Δv/Δt * Δd). I believe, that I can rewrite that as ∫(M * Δd/Δt * Δv), which is simply ∫(M * V * Δv). Once we solve that integral we should get the kinetic energy to be equal to E = (M * V^2)/2

(Please point out any errors or mistakes).

Hoddie54 said:

## The Attempt at a Solution

Firstly I substituted 'MA' into Energy = Mass * Acceleration * Displacement.
Acceleration can be rewritten as Δv/Δt, and so I change my formula to be Energy = M * Δv/Δt * displacement. To find the Energy, in respect to the displacement we can make the integral ∫(M * Δv/Δt * Δd). I believe, that I can rewrite that as ∫(M * Δd/Δt * Δv), which is simply ∫(M * V * Δv). .

You can write Δd=VΔt, so you integral is really ∫(M * V * Δv), which is equal to 1/2 M V2 + constant.

ehild

## What is the formula for kinetic energy?

The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass of an object and v is its velocity.

## What does the "f" in the formula f = ma represent?

The "f" in the formula f = ma represents force, which is measured in Newtons (N).

## How is kinetic energy related to the formula f = ma?

Kinetic energy can be derived from the formula f = ma by multiplying both sides by the displacement of the object, which gives us the equation KE = f * d. Since force is equal to mass times acceleration, we can substitute f for ma, which gives us the final formula KE = 1/2 * m * v^2.

## What are the units of measurement for kinetic energy?

The units of measurement for kinetic energy are Joules (J), which is the same unit used for work and energy.

## What are some real-life applications of the formula f = ma and kinetic energy?

The formula f = ma and kinetic energy have many real-life applications, including calculating the energy of moving objects such as cars, airplanes, and projectiles. This formula is also used in sports to calculate the force and energy of athletes in motion. It is also important in engineering and physics to understand the movement and energy of various objects.

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