Compute kinetic energy, gravitational potential energy, and elastic potential energy, and apply Hooke's law to a spring.
Energy is the capacity to do work, and this week introduces the two forms that dominate mechanics. Kinetic energy (KE) is the energy of motion: KE = (1/2)*m*v^2, measured in joules, always positive (since v^2 can never be negative) and growing with the SQUARE of speed -- doubling an object's speed quadruples its kinetic energy, not just doubles it. Gravitational potential energy (PE) is stored energy due to height in a gravitational field: PE = m*g*h, measured relative to whatever reference height you choose to call zero (usually the ground, or a table top -- the CHOICE of zero never affects a calculated change in energy, only where you decide to start counting from).
A third form, elastic potential energy, is stored in a stretched or compressed spring: PE_spring = (1/2)*k*x^2, where k is the spring constant (how stiff the spring is, in N/m) and x is the distance stretched or compressed from its natural length. This comes from Hooke's law, which says the force a spring exerts is proportional to how far it is displaced: F = k*x. A stiffer spring (larger k) both pushes back harder for the same stretch AND stores more energy for that same stretch.
Mastery looks like: They correctly compute kinetic energy, gravitational potential energy, and elastic potential energy given the relevant quantities, and state Hooke's law.
Common stumbles: Forgetting to square the velocity in the kinetic energy formula; forgetting to square x in the elastic potential energy formula (mixing it up with the linear F=kx).