Velocity

College/University

Definition

Tells you the rate of change of position of an object. It is speed with a direction attached to it. Commonly used to define how fast an object is moving, such as calculations that involve a car driving down a road. To make the car's speed a velocity, it should also specify which direction it is heading.

Worked examples

\(\vec{v} = 60 \) km/h north\(\)

The magnitude (60 km/h) gives the speed; the direction (north) makes it velocity.

\(v = \frac{\Delta x}{\Delta t} = \frac{150 \) m\(}{5 \) s\(} = 30 \) m/s east\(\)

Change in position divided by change in time, with direction specified.

Common mistakes

\(v = 50 \) km/h\(\) → \(v = 50 \) km/h south\(\) Velocity requires a direction; without it you only have speed.
A car going 40 mph around a curve has constant velocity → velocity changes because direction changes Velocity is a vector; changing direction means velocity changes even if speed stays constant.
\(v = \frac{d}{t}\) (using total distance) → \(v = \frac{\Delta x}{\Delta t}\) (using displacement) Velocity uses displacement (straight-line change in position), not total distance traveled.

Where you'll use it next

Velocity is the foundation for studying acceleration, momentum, and kinematic equations in physics. You'll use it in calculus when derivatives describe instantaneous rates of change and in vector analysis.

Found in 1 StudyPug lesson

Position, Velocity, and Acceleration as Derivatives

Calculus 1

Discover how taking derivatives of a position function gives velocity and acceleration, and how their signs describe motion.

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