Velocity

Velocity is the rate of change of an object's displacement (its position) with respect to time. Unlike speed, velocity is a vector quantity, meaning it carries both a magnitude (how fast) and a direction (which way). A car traveling at 60 km/h north has a different velocity than one traveling at 60 km/h south, even though both have identical speed. The Velocity Calculator computes this value from displacement and time inputs.

This distinction matters throughout physics: average velocity is calculated using displacement (the straight-line distance between start and end points, with direction), not total distance traveled, which is what the related Speed Calculator uses instead. An object that travels in a full circle and returns to its starting point has an average velocity of zero, even though it covered real distance and had nonzero average speed the entire time.

Velocity is also the foundation for understanding Acceleration, since acceleration is defined purely in terms of how velocity changes over time. Any change in an object's speed, direction, or both corresponds to acceleration, linking velocity directly to Newton's Second Law and the forces that produce motion.

v = d ÷ t

Where v is velocity (in meters per second, m/s), d is displacement (in meters, m, with direction), and t is time (in seconds, s).

A cyclist travels 300 meters due east in 60 seconds. Their average velocity is:

v = d ÷ t = 300 m ÷ 60 s = 5 m/s east

If instead the cyclist rode 300 meters east and then 300 meters back west over the same 60 seconds, total displacement would be zero, giving an average velocity of 0 m/s — even though the average speed (using total distance of 600 m) would still be 10 m/s.

• A vector, not a scalar: velocity always includes direction, which is what separates it fundamentally from speed.
• Uses displacement, not distance: average velocity is calculated from the net change in position, so looping back to a starting point yields zero average velocity regardless of distance covered.
• Instantaneous vs. average: average velocity covers an entire time interval, while instantaneous velocity describes the rate of change of position at a single moment (found using calculus in advanced treatments).
• Directly tied to Acceleration: any change in velocity, whether in magnitude or direction, means the object is accelerating.
• Direction is relative to a chosen reference: velocities are only meaningfully positive or negative once a positive direction has been defined for the situation being analyzed.