Concept Library / Kinematics

Velocity

Velocity is the rate of change of position.

For uniform motion, the constant velocity equals the displacement divided by any chosen time interval:

v = \frac{Δ s}{Δ t}

For non-uniform motion, $\frac{Δ s}{Δ t}$ is the average velocity over the interval. Instantaneous velocity is developed separately through the limiting/tangent-gradient idea.

Full explanation

Velocity is the rate of change of position.

For uniform motion, the constant velocity equals the displacement divided by any chosen time interval:

v = \frac{Δ s}{Δ t}

For non-uniform motion, $\frac{Δ s}{Δ t}$ is the average velocity over the interval. Instantaneous velocity is developed separately through the limiting/tangent-gradient idea.

Velocity answers: how quickly and in which direction is the position changing?

In one-dimensional motion, the sign of velocity shows whether position is increasing or decreasing. Positive velocity means $s$ increases; negative velocity means $s$ decreases.

Formula / representation

For uniform motion:

v = \frac{Δ s}{Δ t}

Graph representation:

gradient of a straight $s$ - $t$ graph gives constant velocity
horizontal $v$ - $t$ graph shows constant velocity

Units

m s^{- 1}

Common misconceptions

Treating velocity as speed without direction.
Thinking negative velocity means slowing down.
Using total distance in the numerator when calculating velocity.

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