Displacement velocity and acceleration

Displacement, average velocity, and average acceleration form the foundation of kinematics.

Key Definition Displacement is a vector that describes the change in position; it depends only on start and end points, not the path taken.

Average velocity equals the displacement divided by the time interval over which it occurs.

$v_{\mathrm{avg}}$ = Δx / Δt

Average acceleration equals the change in velocity divided by the time interval over which it occurs.

$a_{\mathrm{avg}}$ = Δv / Δt

Both average velocity and average acceleration are vectors whose signs encode direction along the chosen axis.

Acceleration does not require a change in speed — a change in direction alone is sufficient.

Understanding the sign relationship between velocity and acceleration reveals whether an object is speeding up (same sign) or slowing down (opposite signs).

When averages are taken over very small time intervals, they approximate instantaneous values, which appear graphically as the slopes of tangent lines on position-time or velocity-time graphs.

Mastering these distinctions — distance versus displacement, speed versus velocity, and average versus instantaneous — prevents the most common exam errors in kinematics.