Please help, Express kinetic energy in terms of m and p?

[belleamie]

Hi, I think my brain froze and I'm not seeing it
the problem is

the momentum is defined as
p=mv=m(dx/dt)
express the kinetic energy in terms of m and p

~ Now I know kinetic = T= (1/2)mv^2
and that P=mv
I figured that it must be t= (1/2)p^2
till i realized that I'm missing in terms of m. I just got stumped

 

[Theoretician]

T= (1/2)p^2

You know p=mv, so p^2 gives (mv)^2

T=/= (1/2)(mv)^2

where =/= represents 'is not equal to'

I suspect that you will kick yourself when it dawns on you.

 

[Ene Dene]

p=mv -> v=p/m

T=1/2*m*v^2

T=1/2*m(p/m)^2 -> T=1/2((p^2)/m)