A child is swinging on a swing. Which of the following is correct for the child?

Think it through first, then pick an option.

a the kinetic energy is greatest at the highest height
b the velocity is least at the equilibrium position
c the potential energy increases in either direction from the equilibrium position
d the total energy is less at the highest height than at the equilibrium position

Answer and explanation

Correct answer: c the potential energy increases in either direction from the equilibrium position

A swing behaves like the pendulum: at equilibrium it is lowest, so potential energy is least there and rises in either direction. At the highest point the speed and kinetic energy are zero, at equilibrium the speed is greatest, and the total energy is the same everywhere.

Why the other options are wrong

a the kinetic energy is greatest at the highest height: This is not the answer: A swing behaves like the pendulum: at equilibrium it is lowest, so potential energy is least there and rises in either direction. At the highest point the speed and kinetic energy are zero, at equilibrium the speed is greatest, and the total energy is the same everywhere.
b the velocity is least at the equilibrium position: This is not the answer: A swing behaves like the pendulum: at equilibrium it is lowest, so potential energy is least there and rises in either direction. At the highest point the speed and kinetic energy are zero, at equilibrium the speed is greatest, and the total energy is the same everywhere.
d the total energy is less at the highest height than at the equilibrium position: This is not the answer: A swing behaves like the pendulum: at equilibrium it is lowest, so potential energy is least there and rises in either direction. At the highest point the speed and kinetic energy are zero, at equilibrium the speed is greatest, and the total energy is the same everywhere.