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Mechanics
Mechanics

Kinematic Equation 4

x=x0+12(v0+v)tx = x_0 + \frac{1}{2}(v_0 + v)t

Displacement using average velocity.

Variables

x
Final position
Position at time t
m
x₀
Initial position
Initial position
m
v₀
Initial velocity
Initial velocity
m/s
v
Final velocity
Final velocity
m/s
t
Time
Elapsed time
s

Derivation

Average velocity = (v₀ + v)/2, so x - x₀ = v_avg × t.

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Common questions

What is the Kinematic Equation 4 formula?

Kinematic Equation 4 is written x = x₀ + 1/2(v₀ + v)t. Displacement using average velocity. It belongs to Mechanics, under Kinematics.

What are the units in x = x₀ + 1/2(v₀ + v)t?

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

How is the Kinematic Equation 4 formula derived?

Average velocity = (v₀ + v)/2, so x - x₀ = v_avg × t. The result is x = x₀ + 1/2(v₀ + v)t.