Kinematic Equation 3

v^2 = v_0^2 + 2a(x - x_0)

Relates velocity to position without explicit time dependence.

Variables

Final velocity

Velocity at position x

m/s

v₀

Initial velocity

Velocity at position x₀

m/s

Acceleration

Constant acceleration

m/s²

Final position

x₀

Initial position

Derivation

Eliminate t from kinematic equations 1 and 2.

Your notes

0/5000

Check value

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v₀ = 5 m/s (Initial velocity)
a = 4 m/s² (Acceleration)
x = 3 m (Final position)
x₀ = 2 m (Initial position)

Result: v = 5.7445626 m/s

Other mechanics formulas with the same quantities

Acceleration (Kinematics) shares Acceleration
Free Fall (Kinematics) shares Initial velocity
Projectile Range (Kinematics) shares Initial velocity
Projectile Maximum Height (Kinematics) shares Initial velocity
Projectile Time of Flight (Kinematics) shares Initial velocity
Newton's Second Law (Dynamics) shares Acceleration

Where this formula is listed

Mechanics formulas, under Kinematics, alongside Velocity and Average Velocity.
In the mechanics list it comes after Kinematic Equation 2 and before Kinematic Equation 4.
Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Kinematic Equation 3 formula?

Kinematic Equation 3 is written v² = v₀² + 2a(x − x₀). Relates velocity to position without explicit time dependence. It belongs to Mechanics, under Kinematics.

What are the units in v² = v₀² + 2a(x − x₀)?

In SI units, v is final velocity, measured in m/s; v₀ is initial velocity, measured in m/s; a is acceleration, measured in m/s²; x is final position, measured in m; x₀ is initial position, measured in m.

How is the Kinematic Equation 3 formula derived?

Eliminate t from kinematic equations 1 and 2. The result is v² = v₀² + 2a(x − x₀).