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Mechanics
Mechanics

Kinematic Equation 3

v2=v02+2a(x−x0)v^2 = v_0^2 + 2a(x - x_0)

Relates velocity to position without explicit time dependence.

Variables

v
Final velocity
Velocity at position x
m/s
v₀
Initial velocity
Velocity at position x₀
m/s
a
Acceleration
Constant acceleration
m/s²
x
Final position
Final position
m
x₀
Initial position
Initial position
m

Derivation

Eliminate t from kinematic equations 1 and 2.

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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).