Velocity

Also called Instantaneous velocity

Velocity is a vector that gives both how fast an object is moving and in which direction. Used with no qualifier it means instantaneous velocity, the rate of change of position at a single moment, measured in meters per second.

Written $\vec{v}$ , or just $v_x$ once a positive direction along an axis has been fixed. Units are meters per second. Say velocity with no qualifier and you mean the instantaneous value, the rate of change of position at one moment: $v_x = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}$ , which calculus courses write as $dx/dt$ .

On a position-versus-time graph, instantaneous velocity is the slope of the line tangent to the curve at that point, which the AP Physics 1 CED states in EK 1.3.A.4.i. A steeper tangent means faster, and a negative slope means motion in the negative direction.

Constant speed is not constant velocity. Velocity changes whenever its magnitude changes, its direction changes, or both, so a car rounding a bend at a steady 20 m/s is accelerating the whole way around. That distinction decides most circular-motion and equilibrium questions.

A velocity of $-8$ m/s has magnitude 8 m/s. Magnitudes are never negative; the minus sign is the direction, and once a positive axis is declared it is the only direction information a one-dimensional vector needs.

The kinematic equations guide owns solving for it, and topic 1.3 Representing Motion covers reading it off a graph.

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