What is the kinetic energy of a moving material point of mass m at the moment when its momentum is equal to p?

Path p is the momentum of a material point moving at a certain speed v and having a certain mass m. Then the momentum of this point will be equal to p = m * v. Hence, the speed of a material point is equal to:

v = p / m.

We find the kinetic energy by the formula: Eк = m * v ^ 2 / 2. Substituting there the value of the speed found above, we get:

Eк = m * v ^ 2/2 = m * p ^ 2 / (m ^ 2 * 2) = p ^ 2 / (2 * m).

In this case, the SI units of measurement must be observed:

Impulse = kg * m / s, mass – kg, energy – Joule.

Answer: the kinetic energy of the point will be equal to Eк = p ^ 2 / (2 * m).