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Mechanics

Kinematic Equation 2

x=x0+v0t+12at2x = x_0 + v_0 t + \frac{1}{2}at^2

Relates position to initial conditions, acceleration, and time.

Variables

x
Final position
Position at time t
m
x₀
Initial position
Position at t=0
m
v₀
Initial velocity
Velocity at t=0
m/s
a
Acceleration
Constant acceleration
m/s²
t
Time
Elapsed time
s

Derivation

Integrate v = v₀ + at: x = ∫v dt = v₀t + ½at² + x₀.

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Common questions

What is the Kinematic Equation 2 formula?

Kinematic Equation 2 is written x = x₀ + v₀ t + 1/2at². Relates position to initial conditions, acceleration, and time. It belongs to Mechanics, under Kinematics.

What are the units in x = x₀ + v₀ t + 1/2at²?

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; a is acceleration, measured in m/s²; t is time, measured in s.

How is the Kinematic Equation 2 formula derived?

Integrate v = v₀ + at: x = ∫v dt = v₀t + ½at² + x₀. The result is x = x₀ + v₀ t + 1/2at².