Question

Question #b123c

Answer 1

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`