MYTUTOR SUBJECT ANSWERS

414 views

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 F*x = 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/dt

F = m*dv/dt

Putting this in our integral:

int(F*dx) = int (m * dv*dx/dt)

We also know that v = dx/dt.

Therefore int(m*dv*dx/dt) = int(m*dv*v) = 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.

Vandan P. Mentoring -Oxbridge Preparation- tutor, A Level Physics tut...

2 years ago

Answered by Vandan, an A Level Physics tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

57 SUBJECT SPECIALISTS

£24 /hr

Brad D.

Degree: Natural Sciences (Masters) - Durham University

Subjects offered: Physics, Maths

Physics
Maths

“About me: Hey everyone, I'm Brad! I'm studying for a Masters degree in Natural Sciences at Durham, specializing inMaths and Physics. Even while studying at school, I loved the sciences, and I loved being able to help people fully come...”

£22 /hr

Abi R.

Degree: Engineering (Bachelors) - Exeter University

Subjects offered: Physics, Maths+ 3 more

Physics
Maths
Geography
Design & Technology
-Personal Statements-

“About me: I'm in my first year at the University of Exeter studying Mechanical Engineering. My favourite subjects are Maths & Science and my physics teacher is who inspired me to really love teaching others. He was great at using ana...”

£24 /hr

James L.

Degree: Medical Sciences (Bachelors) - Exeter University

Subjects offered: Physics, Science+ 3 more

Physics
Science
Maths
Chemistry
Biology

“Hi, I'm James, a 2nd year Medical Science student. I'm really passionate about science, and I hope i can share some of it with you! ”

About the author

£26 /hr

Vandan P.

Degree: Physical Natural Sciences (Bachelors) - Cambridge University

Subjects offered: Physics, Science+ 6 more

Physics
Science
Maths
Further Mathematics
Chemistry
.STEP.
.MAT.
-Oxbridge Preparation-

“I am a second year undergraduate at Corpus Christi College Cambridge. I am studying Natural Sciences. In my first year I did Physics, Chemistry, Computer Science and Maths and passed with first class honours....”

You may also like...

Posts by Vandan

How to sum an arithmetic progression?

What is sin(x)/x for x =0?

Why is Kinetic Energy mv^2/2?

Other A Level Physics questions

What determines the frequency of oscillation of a (loaded) spring?

What is the force on a moving charged particle in a magnetic field, and why is no work done by this force when it accelerates the particle?

How does stimulated emission work?

What does the double slit experiment tell us about light?

View A Level Physics tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok