Calculate the velocity of a falling object from time or distance. Speed context chart, velocity build-up tables, Mach number, kinetic energy, and momentum analysis.
The velocity of a freely falling object increases by g ≈ 9.81 m/s every second on Earth. After 1 second, it is traveling at 35.3 km/h; after 3 seconds, at 105.9 km/h; after 10 seconds, at 353 km/h. The relationship v = gt (from time) or v = √(2gh) (from distance) governs all free-fall scenarios.
Understanding fall velocity is critical in many contexts: forensic science (estimating fall heights from impact evidence), sports (terminal velocity in skydiving), ballistics (projectile impact speed), and safety engineering (designing fall protection systems). The velocity determines the kinetic energy at impact, which in turn determines the damage potential.
This calculator computes fall velocity from either time or distance, provides speed context (how it compares to walking, driving, sound), generates velocity build-up tables, and calculates kinetic energy and momentum for impact analysis. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Velocity calculations require choosing the right formula (v = gt vs v = √(2gh)), converting between m/s, km/h, and mph, and calculating derived quantities like kinetic energy and Mach number. This calculator handles both modes with visual speed comparisons that contextualize the numbers. Keep these notes focused on your operational context.
From time: v = v₀ + gt From distance: v = √(v₀² + 2gd) Kinetic Energy: KE = ½mv² Momentum: p = mv Mach Number: M = v / 343 Conversions: km/h = m/s × 3.6 mph = m/s × 2.237 ft/s = m/s × 3.281
Result: 29.43 m/s (106 km/h)
v = 0 + 9.81 × 3 = 29.43 m/s = 106.0 km/h = 65.8 mph. For a 1 kg object: KE = ½ × 1 × 29.43² = 433 J, momentum = 29.43 kg·m/s.
In accident reconstruction and forensic science, impact velocity is the single most important parameter. It determines the kinetic energy available for deformation, the peak forces during collision, and the severity of injury. The formula v = √(2gh) directly connects a measurable quantity (fall height) to the critical output (impact speed).
Human perception of speed is poor at extreme values. A fall from a 10-story building (30 m) produces an impact at 87.6 km/h — equivalent to a highway-speed car crash. Yet the fall takes only 2.5 seconds, during which the falling person covers distance at an accelerating rate. Protective equipment must arrest this speed in a controlled manner.
For everyday falls, Newtonian mechanics is perfectly adequate. But for extreme scenarios — like particles falling into neutron stars or black holes — relativistic effects become important when v approaches c (3×10⁸ m/s). At v = 0.1c, relativistic corrections are about 0.5%; at v = 0.5c, they are 15%. The free-fall velocity at a neutron star's surface can reach 0.5c, making relativistic treatment essential.
Without air resistance, velocity increases indefinitely (limited only by relativity at extreme values). With air resistance, terminal velocity limits speed: about 55 m/s (200 km/h) for a belly-down skydiver, up to 90 m/s (320 km/h) head-down.
v = v₀ + gt works when you know the fall time. v = √(v₀² + 2gd) works when you know the fall distance. Both give the same answer — they are derived from the same kinematic equations. Use whichever matches your known data.
Kinetic energy (½mv²) determines the total energy that must be absorbed on impact. Since KE ∝ v², doubling speed quadruples impact energy. A 100 km/h impact has 4× the energy of a 50 km/h impact for the same mass.
Mach number is velocity divided by the local speed of sound (343 m/s at sea level, 15°C). Mach 1 is the speed of sound. Only extreme falls — from stratospheric altitude in thin air — can approach or exceed Mach 1 in free fall.
Yes, in ideal free fall (no air resistance), velocity increases linearly: v = gt. The graph of velocity vs time is a straight line with slope g. This is a direct consequence of constant gravitational acceleration.
Rearrange v = √(2gh) to h = v²/(2g). For example, to reach 100 km/h (27.78 m/s): h = 27.78²/(2×9.81) = 39.3 m (about 13 stories). Use the distance-velocity table for quick lookups.