Plain-English Meaning
Moving things have energy — kinetic energy. The faster you go, the more energy you have, and speed has a squared effect: doubling your speed means four times the kinetic energy. This is why car crashes at 60 mph are four times more energetic than at 30 mph.
Mechanics questions usually become easier once you identify whether the problem is about force balance, kinematics, energy, or conservation.
Deeper Explanation
KE = ½mv² comes from the work–energy theorem: W_net = ΔKE. The ½ appears when you integrate F dx = ma dx = m v dv from 0 to v. In 3D, KE = ½m|v|².
Worked Example
Problem: A 1200 kg car travels at 30 m/s. Calculate its kinetic energy.
- KE = ½mv²
- KE = ½ × 1200 × (30)²
- KE = 600 × 900
- KE = 540,000 J
Result: KE = 540 kJ
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At A Glance
Category: Mechanics
Levels covered: High School, College, Masters, PhD
Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.