1.1 Position, Velocity, and Acceleration

Position and Displacement

Position describes an object's location relative to a chosen origin. Displacement is the change in position, a vector with both magnitude and direction, calculated as final position minus initial position. Displacement differs from distance, which is the total path length traveled and is always positive, regardless of direction changes.

Velocity: Average and Instantaneous

Average velocity equals displacement divided by elapsed time, a vector quantity. Average speed is total distance divided by time, always non-negative. Instantaneous velocity is the velocity at a specific moment, found from the slope of a position-time graph at that point. Velocity's sign indicates direction of motion.

Acceleration

Acceleration is the rate of change of velocity over time, also a vector. It can result from speeding up, slowing down, or changing direction. On a velocity-time graph, acceleration equals the slope. When velocity and acceleration have the same sign, the object speeds up; opposite signs mean it slows down.

Key terms

Position

An object's location relative to a chosen reference point or origin.

Displacement

A vector quantity equal to the change in position (final minus initial); can be positive, negative, or zero.

Average velocity

Displacement divided by elapsed time; a vector quantity that can be negative.

Instantaneous velocity

The velocity at a specific moment in time, given by the slope of the tangent line on a position-time graph.

Acceleration

The rate of change of velocity over time; a vector quantity equal to the slope of a velocity-time graph.

Try an AP-style question

A student walks 3 m east, then 4 m west. What are the displacement and distance?

1. Displacement 7 m west; distance 1 m
2. Displacement 5 m west; distance 7 m
3. Displacement 1 m west; distance 7 m
4. Displacement 1 m east; distance 7 m