Concept Library / Kinematics

Instantaneous Velocity

Instantaneous velocity is the velocity of an object at a particular instant. On a position-time graph, it is the gradient of the tangent at that instant.

Full explanation

Instantaneous velocity is the velocity of an object at a particular instant. On a position-time graph, it is the gradient of the tangent at that instant.

Average velocity describes a complete time interval. Instantaneous velocity describes the local motion at one moment. A tangent estimates the gradient of the curve at that point; using two widely separated points instead gives an average velocity over the interval.

Formula / representation

For calculus-based treatments,

v = \frac{d s}{d t} .

For IB graphical work, draw a tangent at the required point and calculate

v \approx \frac{Δ s_{tangent}}{Δ t_{tangent}} .

Instantaneous speed is the magnitude $| v |$ .

Common misconceptions

Joining the origin to the point instead of drawing a tangent.
Using two points on the curve rather than two well-separated points on the tangent.
Reporting a negative velocity as a negative speed.
Omitting units or using position units rather than $m s^{- 1}$ .

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