EQUATION

1D Kinematic Equations (Constant Acceleration)

Three interrelated equations — v = v_0 + at, d = v_0·t + ½at², v² = v_0² + 2ad — collectively cover every constant-acceleration problem

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The equation

EQ.KINEMATIC-EQUATIONS
v = v_0 + at,\; d = v_0 t + \tfrac{1}{2}at^2,\; v^2 = v_0^2 + 2ad
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What it solves

Three interrelated equations — v = v_0 + at, d = v_0·t + ½at², v² = v_0² + 2ad — collectively cover every constant-acceleration problem. Each equation omits one of the five quantities {v_0, v, a, t, d}, so you pick whichever one does not contain the unknown you are not given.

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When to use it

Any straight-line motion with constant acceleration: free fall, braking, conveyor problems, incline problems (before accounting for variable friction).

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When NOT to use it

Do not apply when acceleration changes with velocity or time — e.g., drag-dominated motion or rocket burn with varying thrust. For 2D motion, apply each equation independently per component.

§ 05

Common mistakes

Trying to use all three equations when one suffices. Forgetting that d is net displacement, not total distance, if the object reverses. Choosing the wrong equation and then solving for an unused variable.

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Topics that use this equation

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Problems using this equation