Use the concepts of kinetic energy and potential energy to describe the motion of a child on a swing. why does the child need a push from time to time?

The kinetic energy refers to the energy that a body has due to its speed, depends on it, the more speed the more kinetic energy will have.

The potential energy depends only on the position, specifically, the height with respect to a referential points, the more height, more potential energy will have.

These two type of energy are always exchanging from one to another, depending on the movement. When the child is swinging, he will reach a maximum point, maximum amplitude of the movement, when that point it's reached, the swing will go back. This happens because the exchange of energies.

When the swing is at maximum amplitude, the extreme points, there the kinetic energy reach the zero level, because the swing stops instantaneously. At that point of maximum amplitude, the potential energy is the higher possible, because all missing energy for kinetic is transformed as potential, this is the Conservation of Energy Theorem.

So, while the swing is moving, these two energies exchanges. The point where the potential energy is null, is the equilibrium point, when the swing passes through that point, the kinetic energy is maximum, because at that equilibrium point, the swing's height is zero.

However, this transformation of energy doesn't last forever, because it's not a perfect and controlled environment, so, the energy is constantly also transformed as heat, due to the friction of the swing. This means that after a while, the swing will stop, because the energy is producing heat, constantly. That's why the child needs to push from time to time, because the heat is subtracting energy from the system, so new input energy is needed to continue the movement.