Uniformly Accelerated Motion - Velocity Squared Equation
Uniformly Accelerated Motion - Velocity Squared Equation
\[v^2 = v_0^2 + 2ad\]
Variables
v = final velocity (m/s)
v0 = initial velocity (m/s)
a = acceleration (m/s²)
d = displacement (m)
Description
What is this formula?
This equation relates final velocity, initial velocity, acceleration, and displacement for motion with constant acceleration without requiring time.
When to use it
Use this formula when the time variable is unknown or unnecessary and the motion occurs with constant acceleration.
Example
If an object starts at 4 m/s, accelerates at 3 m/s², and travels 10 m:
v² = 4² + 2 × 3 × 10 = 76
v = ?76 = 8.72 m/s
Applications
Motion analysis, automotive engineering, braking calculations, robotics, and classical mechanics.
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