Kinematic Equation 2

x = x_0 + v_0 t + \frac{1}{2}at^2

Relates position to initial conditions, acceleration, and time.

Variables

Final position

Position at time t

x₀

Initial position

Position at t=0

v₀

Initial velocity

Velocity at t=0

m/s

Acceleration

Constant acceleration

m/s²

Time

Elapsed time

Derivation

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

Your notes

0/5000

Check value

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

Result: x = 67 m

Other mechanics formulas with the same quantities

Free Fall (Kinematics) shares Initial velocity, Time
Acceleration (Kinematics) shares Acceleration
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 1 and before Kinematic Equation 3.
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 2 formula?

Kinematic Equation 2 is written x = x₀ + v₀t + (1/2)at². Relates position to initial conditions, acceleration, and time. It belongs to Mechanics, under Kinematics.

What are the units in x = x₀ + v₀t + (1/2)at²?

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 + v₀t + (1/2)at².