Instantaneous velocity and speed

Instantaneous velocity, v = dx/dt, is the value the average velocity approaches as the time interval shrinks to zero.

On a position-time (x-t) graph, the slope of the tangent drawn to the curve at any instant gives the velocity at that instant.

A straight x-t line means constant velocity; a curved x-t graph means the velocity is changing.

Instantaneous speed is the magnitude of instantaneous velocity. This equality holds at an instant, not for averages over an interval.

Velocity can be found numerically (by shrinking Δt in a table of values) or by calculus when x is given as a function of t.

A negative velocity only says the body is moving towards the negative x-direction; it says nothing about whether it is slowing down.