Momentum and kinetic energy.

Force=Rate of change of momentum
= (mv-mu)/t = ma

Energy(= Work) =Force x distance moved

If distance is s then v(sqd)=u(sqd) + 2as
so if u=0, s= v(sqd)/2a

Placing this in the energy expression
Energy = ma x s = ma x v(sqd)/2a = 1/2 mv(sqd)

Neither.

force = mass x acceleration

But, energy and momentum are conserved.

We should add of course that

momentum = mass x velocity

Yes, but if I fall and my head hits the ground, is it hitting it as Mass x velocity or 1/2 mass x velocity squared? If a bat hits a ball is it hitting it with the force of momentum or kinetic energy? Isn't kinetic energy 1/2mass x velocity squared?

Coluber,

Your question is imprecise.

Your head is hitting the ground with

a velocity v
a momentum mv
a force mg (if you fall)
an energy 1/2 mv(sqd)

each of these are dfferent physical combinations in terms of their reducibility to products of the three basic entitities MASS, LENGTH & TIME

Energy and momentum are two separate things (if I recall my physics correctly).

In any system, total momentum and total energy will remain constant. But you calculate each separately.

In your example of your head hitting the ground, your head has a certain momentum and a certain kinetic energy.

When your head hits, some momentum will be transferred to the earth. Some kinentic energy will be transferred as well, but some kinetic energy will also be converted to heat (from friction), sound waves, etc.

if you fall,
a force will hit you equal to 0 - (ur initial momentum) all over the length of time it takes for your momentum to be zero..

work is change in kinetic energy,, so the earth does work on you (negative work)
the distance required to decelerate you to a stop is almost zero coz it's instantaneous.

so the force that will hit you is work/distance... since the distance is very small, the force is large, that explains why it hurts (if you fall at high velocitie)..