What is the equation for the change in kinetic energy of a particle?

What is the equation for the change in kinetic energy of a particle?

• A. ΔE = m x a
• B. ΔE = F x d
• C. ΔE = q x V
• D. ΔE = q x d

Answer: (C)

The change in a particle’s kinetic energy comes from the work done on it by forces. Work is the energy transferred by a force along the path, and when the force is constant and acts in the same direction as the motion, the work equals force times distance: W = F d. By the work-energy theorem, the change in kinetic energy ΔK equals the work done, so ΔE = F d. This captures how applying a force over a distance changes the particle’s speed. The other expressions don’t describe kinetic-energy change: m × a is Newton’s second law giving the force, not the energy; q × V relates to electric potential energy (U = qV) rather than kinetic energy; and q × d isn’t a standard energy relation.

The change in a particle’s kinetic energy comes from the work done on it by forces. Work is the energy transferred by a force along the path, and when the force is constant and acts in the same direction as the motion, the work equals force times distance: W = F d. By the work-energy theorem, the change in kinetic energy ΔK equals the work done, so ΔE = F d. This captures how applying a force over a distance changes the particle’s speed.

The other expressions don’t describe kinetic-energy change: m × a is Newton’s second law giving the force, not the energy; q × V relates to electric potential energy (U = qV) rather than kinetic energy; and q × d isn’t a standard energy relation.