Why does kinetic energy increase as velocity squared?

[JamSmith]

The formula for kinetic energy is E=[1/2]mv^2 and the formula for momentum is P=mv. I ran into these in physics class long ago and was really bothered by the first formula. How can energy go up as the square of the velocity?

[studiot]

There was a long discussion about this recently, so it obviously bothers some beginners.

 

http://www.scienceforums.net/topic/59887-help-in-explaining-formula-of-kinetic-energy/page-2?hl=%2Bkinetic+%2Benergy#entry949583

 

my contribution started at post#39

[JamSmith]

There was a long discussion about this recently, so it obviously bothers some beginners.

 

http://www.scienceforums.net/topic/59887-help-in-explaining-formula-of-kinetic-energy/page-2?hl=%2Bkinetic+%2Benergy#entry949583

 

my contribution started at post#39

Thanks. I have found much more clues to solve my doubts.

[Sriman Dutta]

Just showing how the KE formula is derived:

 

Consider a moving body with initial velocity v and final velocity 0. Let the distance travelled be S. Let the retardation force be F and deceleration be d.

Then, 0^2=v^2+2aS or a=-v^2/2S

So F=md=m(-a)=mv^2/2S

So work done = FS=mv^2/2

But work done = KE

So KE=0.5mv^2