Kinematic v² Relation
Links initial velocity, final velocity, and displacement without requiring time
The equation
What it solves
Links initial velocity, final velocity, and displacement without requiring time. The equation is the right choice whenever time is unknown and you are asked for a velocity or a distance.
When to use it
Constant-acceleration straight-line motion where time is either unknown or irrelevant. Classic applications: stopping distance, launch speed from fall height.
When NOT to use it
Requires constant acceleration; invalid for drag-dominated problems where a changes with speed. Also fails in 2D unless applied component-by-component.
Common mistakes
Mixing up v and v_0 — the convention is v_0 initial, v final. Forgetting to take the square root when solving for v. Using total displacement d when the object reverses direction mid-path.