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Velocity
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Sources & Methodology
Formulas verified against NIST unit definitions, Khan Academy Physics, and BIPM SI unit standards.
Khan Academy — What is Velocity?
Curriculum reference for velocity definition, formula v = d/t, distinction between speed and velocity, and average velocity calculations.
NIST Special Publication 811 — Guide to SI Units
Official NIST reference for SI unit definitions and conversion factors used for m/s, km/h, mph, ft/s, and knot conversions.
NIST — Speed of Light (CODATA)
NIST CODATA value for speed of light c = 299,792,458 m/s (exact), used as reference for context comparisons.
Methodology: All inputs converted to m/s base unit before calculation. v (m/s) = d (m) / t (s). Distance conversions: 1 km = 1000 m, 1 mi = 1609.344 m, 1 ft = 0.3048 m, 1 nmi = 1852 m. Time conversions: 1 min = 60 s, 1 h = 3600 s. Velocity output conversions: ×3.6 = km/h, ×2.23694 = mph, ×3.28084 = ft/s, ×1.94384 = knots.
⏱ Last reviewed: March 2026
How to Calculate Velocity — Formula, Units & Examples
Velocity measures how fast an object moves and in what direction. Average velocity is the total displacement divided by the total time elapsed. In everyday use, velocity magnitude equals speed and is calculated using the simple formula v = d/t.
The Three Velocity Formulas
v = d / t d = v × t t = d / v
v = velocity (m/s, km/h, mph, ft/s, knots)
d = distance (m, km, miles, feet, nautical miles)
t = time (seconds, minutes, hours)
Example 1 — Usain Bolt’s 100m world record (9.58 s):
v = 100 m / 9.58 s = 10.44 m/s = 37.58 km/h = 23.35 mph
Example 2 — Distance covered by a car at 120 km/h in 2.5 hours:
d = 120 km/h × 2.5 h = 300 km
d = distance (m, km, miles, feet, nautical miles)
t = time (seconds, minutes, hours)
Example 1 — Usain Bolt’s 100m world record (9.58 s):
v = 100 m / 9.58 s = 10.44 m/s = 37.58 km/h = 23.35 mph
Example 2 — Distance covered by a car at 120 km/h in 2.5 hours:
d = 120 km/h × 2.5 h = 300 km
Velocity Unit Conversion Table
| m/s | km/h | mph | ft/s | knots |
|---|---|---|---|---|
| 1 | 3.600 | 2.237 | 3.281 | 1.944 |
| 10 | 36.00 | 22.37 | 32.81 | 19.44 |
| 27.78 | 100 | 62.14 | 91.13 | 53.96 |
| 44.70 | 160.93 | 100 | 146.67 | 86.90 |
| 343 | 1235 | 767.3 | 1125 | 667.2 |
Reference Speeds for Context
| Object / Event | Speed (m/s) | km/h | mph |
|---|---|---|---|
| Walking (average adult) | 1.4 | 5.0 | 3.1 |
| Usain Bolt (100m WR) | 10.44 | 37.6 | 23.4 |
| Cheetah (top speed) | 29.2 | 105 | 65.2 |
| Highway car (100 km/h) | 27.8 | 100 | 62.1 |
| Commercial aircraft | 250 | 900 | 560 |
| Sound in air (20°C) | 343 | 1235 | 767 |
| Space Shuttle reentry | 7,800 | 28,080 | 17,450 |
| Light in vacuum | 299,792,458 | 1.08×10³ | 6.71×10² |
💡 Speed vs velocity: Speed is a scalar (magnitude only). Velocity is a vector (magnitude + direction). A car completing a 1 km circular track back to its start has average speed = 1000/t m/s but average velocity = 0 (displacement = 0). In physics problems, always check whether you need speed (path length / time) or velocity (displacement / time).
Velocity in Physics Equations
- Kinetic energy: KE = ½mv² — doubling velocity quadruples kinetic energy
- Momentum: p = mv — used in collision and impulse problems
- Kinematic equations: v = v₀ + at, v² = v₀² + 2ad, d = v₀t + ½at²
- Wave speed: v = fλ — frequency times wavelength
- Escape velocity: v = √(2GM/r) — Earth escape velocity = 11,186 m/s
Average Velocity vs Instantaneous Velocity
Average velocity = total displacement / total time. It tells you the overall rate of motion over a whole journey. Instantaneous velocity is the velocity at a specific instant, equal to the derivative of position with respect to time (v = dx/dt in calculus). A car trip’s average velocity might be 80 km/h even though the car stopped at traffic lights and accelerated on motorways — the instantaneous velocity varied throughout but the average tells you the overall pace.
Frequently Asked Questions
Velocity = Distance / Time, or v = d/t. Rearranged: d = v×t and t = d/v. For example, a runner covering 400 m in 50 seconds has velocity = 400/50 = 8 m/s = 28.8 km/h. Velocity is a vector (has direction) but the magnitude is calculated the same way as speed.
Multiply m/s by 3.6 to get km/h. For example, 20 m/s × 3.6 = 72 km/h. To convert km/h back to m/s, divide by 3.6: 72 / 3.6 = 20 m/s. The factor 3.6 comes from 3600 seconds per hour divided by 1000 metres per kilometre.
Multiply mph by 0.44704 to get m/s. For example, 60 mph × 0.44704 = 26.82 m/s. To convert m/s to mph, multiply by 2.23694. Also: 1 mph = 1.60934 km/h = 1.46667 ft/s = 0.86898 knots.
Speed is scalar (magnitude only). Velocity is a vector (magnitude + direction). Speed = distance/time. Velocity = displacement/time. If you drive around a circular track and return to start: average speed = total distance / time (non-zero). Average velocity = 0 because displacement = 0. For straight-line motion in one direction, speed equals velocity magnitude.
Average velocity = total displacement / total time. For uniform acceleration: average velocity = (initial + final velocity) / 2. For a multi-segment trip, sum each displacement (not distance) and divide by total time. Example: drive 60 km east then 20 km west in 2 hours. Displacement = 40 km east. Average velocity = 40/2 = 20 km/h east. Average speed = 80/2 = 40 km/h.
Relative velocity is the velocity of one object as seen by another moving observer. Same direction: vₐₒ = vA − vB. Opposite directions: vₐₒ = vA + vB. For example, two trains at 80 km/h approaching each other have a relative velocity of 160 km/h. A car at 100 km/h overtaking a truck at 80 km/h has a relative velocity of 20 km/h.
Speed of sound in air at 20°C: 343 m/s (1235 km/h, 767 mph). It increases with temperature: v = 331 + 0.6×T (Celsius). In water: ~1480 m/s. In steel: ~5100 m/s. In bone: ~3500 m/s. Sound travels faster in denser, stiffer materials. Mach number = object speed / local speed of sound. Mach 1 = sonic, above Mach 1 = supersonic.
Using kinematics: v = v₀ + a×t (velocity after time t). v² = v₀² + 2×a×d (velocity after distance d). For a car starting from rest (v₀=0) with acceleration 3 m/s² for 10 s: v = 0 + 3×10 = 30 m/s = 108 km/h. After 100 m from rest: v = √(2×3×100) = √600 = 24.5 m/s.
Terminal velocity is reached when drag force equals gravitational force, giving zero net acceleration and constant speed. For a skydiver spread-eagle: approximately 53 m/s (190 km/h). Head-down: approximately 90 m/s (320 km/h). A raindrop has terminal velocity around 9 m/s. Terminal velocity depends on mass, drag coefficient, cross-sectional area, and fluid density.
Earth’s escape velocity is 11,186 m/s (40,270 km/h, 25,020 mph). This is the minimum speed an object needs to escape Earth’s gravitational field without further propulsion. Formula: v𝑒 = √(2GM/r) where G = 6.674×10⁻¹¹ N·m²/kg², M = 5.972×10²⁴ kg (Earth mass), r = 6.371×10⁶ m (Earth radius). The Moon’s escape velocity is 2,380 m/s.
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