Deriving Formula of Kinetic Energy using f = ma

[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).

 

[ehild]

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