velocity

Meaning: Velocity tells how fast and in what direction an object's position changes. Average velocity is total displacement divided by elapsed time. Instantaneous velocity is the limit of that ratio as the time interval shrinks, which is the slope of a position-time graph at a point. Because it is a vector, its sign (in one dimension) or components (in two) carry the direction. Speed is the magnitude of instantaneous velocity.

Equation: v = Δx/Δt, where v is velocity (m/s), Δx is displacement (m), and Δt is elapsed time (s). With constant acceleration, v = v₀ + at, where v₀ is initial velocity (m/s), a is acceleration (m/s²), and t is time (s).

On the MCAT: Expect position-time or velocity-time graphs. The slope of a position-time graph is velocity, and the slope of a velocity-time graph is acceleration. The area under a velocity-time graph is displacement. Projectile questions split velocity into independent horizontal and vertical components. Other questions ask for average velocity over a round trip, which is zero when the object returns to its start.

Common confusion: Students treat velocity and speed as the same. Average speed is total distance over time, while average velocity uses displacement. A runner who completes one lap has nonzero average speed but zero average velocity. Changing direction changes velocity even when speed stays constant.