kinetic energy
Summary
Kinetic energy is the energy an object has because of its motion, K = ½mv². It depends on the square of speed, so doubling speed quadruples kinetic energy. The work-energy theorem says net work on an object equals its change in kinetic energy.
Detail
Meaning: Kinetic energy is the energy of motion. It is a scalar that depends on mass and speed but not on direction, and its value is zero or positive. Net work changes it: positive net work speeds an object up, and negative net work (such as friction) slows it down. For gas molecules, average kinetic energy is proportional to absolute temperature, so gases at the same temperature have the same average kinetic energy per molecule regardless of molecular mass.
Equation: K = ½mv², where K is kinetic energy in joules (J), m is mass in kilograms (kg), and v is speed in meters per second (m/s). The work-energy theorem is Wnet = ΔK = ½mvf² − ½mvi², with Wnet in joules.
On the MCAT: Typical passages involve a ramp, pendulum, or roller coaster. With no friction, mgh at the top converts to ½mv² at the bottom, so v = √(2gh) and mass cancels. With friction, the work done by friction equals the kinetic energy lost. You may be asked to read a K versus v graph, which is a parabola, or to predict how stopping distance changes with speed (doubling speed roughly quadruples it under constant friction).
Common confusion: Students mix kinetic energy with momentum, p = mv. Doubling speed doubles momentum but quadruples kinetic energy. Momentum is a vector and is conserved in collisions with no external force. Kinetic energy is a scalar and is not conserved in inelastic collisions.
Sources
- Physics (Giancoli)
- University Physics (Young and Freedman)
- Fundamentals of Physics (Halliday, Resnick, Walker)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.