Why is Kinetic Energy mv^2/2?

Whilst this proof is beyond the scope of A level physics, it is well within the scope of A level Maths as it relies solely on the chain rule.First let us note that Fx = W where F is force, x is distance and W is work or energy.However if we have a varying force, we must sum the Force in dx sized chunks, ie. W = int ( F dx) and it is from there we get our proof.F = ma (from Newton II)a = dv/dtF = mdv/dtPutting this in our integral:int(Fdx) = int (m * dvdx/dt)We also know that v = dx/dt.Therefore int(mdvdx/dt) = int(mdvv) = int(mv dv).Taking the integral we can see that W = mv2/2 + C where C is dependant on the initial speed we take the work done from. If initial speed is 0 then C also becomes 0 and we get the well known formula.

Answered by Vandan P. Physics tutor

5707 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

Why does a small puddle of water evaporate at room temperature, even though the temperature is way below the boiling point of water?


What is the minimum frequency of electromagnetic radiation needed for a photon to ionise an atom of sodium? ( An atom of sodium has an ionisation energy of 5.15 eV.)


A ball is dropped from rest at a height of 2 metres. Assuming acceleration due to gravity (g) is 10m/s^2 calculate the velocity of the ball just before it hits the floor.


An infared wave has a wavelength of 1.5 x10^–6 m. The speed of this wave is 2.2 × 10^8 m/s. Calculate the frequency of the wave. Give your answer in standard form and to 2 significant figures.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences