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Velocity is a vector quantity that describes both the speed and direction of an object's motion. While speed tells you how fast something is moving, velocity tells you how fast and in which direction. This distinction is crucial in physics — a car traveling at 60 km/h east has the same speed as one traveling at 60 km/h west, but completely different velocities.
The fundamental kinematic velocity equation is v = u + at, where v is final velocity, u is initial velocity, a is constant acceleration, and t is time elapsed. This linear relationship means velocity increases uniformly when acceleration is constant — the hallmark of classical Newtonian mechanics.
Velocity is measured in metres per second (m/s) in SI units, though km/h and mph are common in everyday contexts. Converting: 1 m/s = 3.6 km/h = 2.237 mph. To convert km/h to m/s, divide by 3.6.
Worked example: A train starts from rest (u = 0 m/s) and accelerates at a = 1.5 m/s² for t = 20 seconds. Final velocity v = 0 + 1.5 × 20 = 30 m/s (108 km/h). Average velocity over this interval = (0 + 30)/2 = 15 m/s.
v = u + at
v = u + at
Velocity Formulas Reference
| Formula | Variables | Units |
|---|---|---|
| v = u + at | u = initial, a = accel, t = time | m/s |
| u = v − at | v = final, a = accel, t = time | m/s |
| v_avg = s/t | s = displacement, t = time | m/s |
| v_avg = (u+v)/2 | u = initial, v = final | m/s |
| v² = u² + 2as | SUVAT — omits time | m²/s² |
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.