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Calculate velocity (v = d/t), find distance from speed and time, or determine travel time from speed and distance. Covers average velocity, instantaneous velocity, and kinematic equations used in physics problem-solving.
Velocity is a vector quantity describing the rate of change of position — it has both magnitude (speed) and direction. Average velocity = total displacement / total time. Speed and velocity differ: speed is scalar (magnitude only), while velocity includes direction. A car driving a complete circle returns to start with zero displacement but nonzero distance traveled.
Velocity is one of the most fundamental concepts in classical mechanics, describing how quickly an object changes its position. Unlike speed, which is a scalar quantity (magnitude only), velocity is a vector that includes both magnitude and direction. A car traveling at 60 km/h northward and another at 60 km/h southward have the same speed but opposite velocities.
Average velocity = total displacement / total time elapsed. Displacement is the straight-line distance from start to finish, regardless of the path taken. A runner completing a 400m circular track has traveled 400m distance but zero displacement — and zero average velocity for the complete lap, though their average speed is nonzero.
When acceleration is constant, four kinematic equations relate velocity, acceleration, displacement, and time: (1) v = v₀ + at. (2) x = v₀t + ½at². (3) v² = v₀² + 2ax. (4) x = ½(v₀ + v)t. These four equations, derived from calculus, completely describe motion under constant acceleration. Any three known variables allow calculation of the remaining two.
| Object | m/s | km/h | Note |
|---|---|---|---|
| Walking | 1.4 m/s | 5 km/h | Average adult walking speed |
| Running | 3-6 m/s | 10-22 km/h | Recreational to competitive |
| Highway car | 27.8 m/s | 100 km/h | Freeway speed limit |
| Sound (air, 20°C) | 343 m/s | 1235 km/h | Mach 1 |
| Commercial jet | 250 m/s | 900 km/h | Cruising altitude |
| Space Shuttle (orbit) | 7,800 m/s | 28,000 km/h | Low Earth orbit |
| Light (vacuum) | 3×10⁸ m/s | 1.08×10⁹ km/h | Universal speed limit |
Velocity is always measured relative to a reference frame. A passenger walking at 5 km/h toward the front of a train moving at 200 km/h is moving at 205 km/h relative to the ground. Galilean velocity addition (non-relativistic): v_AB = v_AC + v_CB, where v_AB is velocity of A relative to B. At speeds approaching the speed of light, Einstein special relativity modifies this: v_rel = (v₁ + v₂)/(1 + v₁v₂/c²), preventing any object from exceeding c.
When a falling object reaches terminal velocity, drag force equals gravitational force and acceleration becomes zero — constant velocity is maintained. Terminal velocity depends on: mass, cross-sectional area, drag coefficient, and fluid density. Skydiver in spread position: ~54 m/s (195 km/h). Skydiver in dive: ~90 m/s (320 km/h). Raindrop: 9 m/s. Hailstone: 10-48 m/s depending on size. Terminal velocity = √(2mg/ρCdA) where m=mass, g=gravity, ρ=air density, Cd=drag coefficient, A=cross-sectional area.
1 m/s = 3.6 km/h = 2.237 mph = 1.944 knots. 1 km/h = 0.2778 m/s = 0.6214 mph. 1 mph = 1.609 km/h = 0.4470 m/s. 1 knot = 1.852 km/h = 0.5144 m/s (used in aviation and maritime). Mach number = v/v_sound (343 m/s at sea level, 20°C). Mach 1 = 343 m/s = 1235 km/h. Mach varies with altitude and temperature — aircraft at Mach 1 at 10,000m altitude travel at ~1050 km/h (air is colder, speed of sound lower).
Always ensure units are consistent before calculating. This calculator uses SI units (International System): meters (m) for distance, kilograms (kg) for mass, seconds (s) for time, Newtons (N) for force, Joules (J) for energy, Watts (W) for power, and Pascals (Pa) for pressure. When converting from other unit systems (imperial, CGS), convert all values before entering them into the calculator.
Gravitational acceleration on Earth: g = 9.81 m/s² (standard: 9.80665 m/s²). Speed of light in vacuum: c = 2.998×10⁸ m/s. Universal gravitational constant: G = 6.674×10⁻¹¹ N·m²/kg². Speed of sound in air at 20°C: 343 m/s. Atmospheric pressure at sea level: 101,325 Pa = 1 atm. These constants appear in virtually every branch of physics and engineering.
Physics calculations directly inform engineering safety standards. Stopping distance calculations (kinetic energy / braking force) set speed limits and vehicle safety requirements. Pressure calculations determine pipe and vessel wall thickness in plumbing and industrial equipment. Torque specifications on fasteners prevent structural failures. Centripetal acceleration limits guide road curve design and roller coaster safety. Every safety standard in transportation, construction, and consumer products has physics calculations at its foundation.