Question #b123c

1 Answer
Apr 3, 2017

Answer:

See below

Explanation:

If they have different formulae they are not the same:

  • Vector quantity momentum is #mathbf p = m mathbf v#. Momentum is always conserved in consequence of Newton's 2nd and 3rd Laws.

  • Scalar quantity Kinetic Energy is #T = 1/2 m v^2#. T is conserved, for example, in elastic collisions; but it is not always conserved.

In modern physics, they are often combined as:

#T = p^2/(2m)#

You are right in one sense though. For constant mass, they are both functions of velocity; but:

  • #p propto v#

  • #T propto v^color(red)(2)#

and

  • #T propto p^2#

A more interesting relationship might be, where #x# is displacement:

#(dT)/dx = mv (dv)/dx = ma#