Mechanics
Free Fall
Vertical motion under gravity, neglecting air resistance.
Variables
ym
Height
Vertical position
y₀m
Initial height
Starting height
v₀m/s
Initial velocity
Initial vertical velocity
gm/s²
Gravitational acceleration
≈ 9.8 m/s²
Allowed values: greater than 0
ts
Time
Elapsed time
Derivation
Special case of kinematic equation 2 with a = -g.
Your notes
0/5000
Constants in this formula
Check value
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- y₀ = 2 m (Initial height)
- v₀ = 3 m/s (Initial velocity)
- g = 9.806 65 m/s² (Gravitational acceleration)
- t = 4 s (Time)
Result: y = -64.4532 m
Other mechanics formulas with the same quantities
- Kinematic Equation 1 (Kinematics) shares Initial velocity, Time
- Kinematic Equation 4 (Kinematics) shares Initial velocity, Time
- Projectile Maximum Height (Kinematics) shares Initial velocity, Gravitational acceleration
- Projectile Time of Flight (Kinematics) shares Initial velocity, Gravitational acceleration
- Kinematic Equation 3 (Kinematics) shares Initial velocity
- Weight (Dynamics) shares Gravitational acceleration
Where this formula is listed
- Mechanics formulas, under Kinematics, alongside Velocity, Acceleration and Average Velocity.
- In the mechanics list it comes after Kinematic Equation 4 and before Projectile Range.
- 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 Free Fall formula?
Free Fall is written y = y₀ + v₀t − (1/2)gt². Vertical motion under gravity, neglecting air resistance. It belongs to Mechanics, under Kinematics.
What are the units in y = y₀ + v₀t − (1/2)gt²?
In SI units, y is height, measured in m; y₀ is initial height, measured in m; v₀ is initial velocity, measured in m/s; g is gravitational acceleration, measured in m/s²; t is time, measured in s.
How is the Free Fall formula derived?
Special case of kinematic equation 2 with a = -g. The result is y = y₀ + v₀t − (1/2)gt².