Meaning of KE=1/2m v^2?

 

Hi. Lay person.

I was wondering about a physical meaning to the speed-energy relation.

 

I started from the equivalence between gravity and inertial acceleration. So I hypothesize that there is the same underlying phenomenon at work; given that matter-energy warps space and that warping is gravity, I would speculate that maybe a change in velocity also entails a warping of space.

In particular I thought that if a change in velocity were associated to a warping of space in two dimensions (ie. orthogonal to the direction of the force) it would explain the quadratic relation between speed and the energy required to achieve it.

This (very general) idea might be relatable to the length contraction prediction of SR and it could explain the limit nature of 'c' as an upper boundary to space warping.

 

Gravity has a gradient while inertial acceleration doesn't, but still. Does this idea have any merit? If it's implausible, why?

 

Thanks

KE = 1/2 mv^2 comes directly from the definition of work. The energy added to a system with a constant force through some arbitrary distance can be recast as 1/2 mv^2

 

F dx = ma dx = m (dv/dt) dx = m (dv/dx)(dx/dt) dx = mv dv

 

Integrate that and you get your answer