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 acceleration: Derivative

Calculus 1

We now know that taking the derivative of a function will give us the slope, or the instantaneous rate of change of the function. So what if we take the derivative of a function that models the position of some object moving along a line? It gives us its velocity! And if we differentiate its velocity function? It gives us its acceleration! In this section, we will study the relationship between position, velocity and acceleration using our knowledge of differential calculus.

UniversityUniversity