Kinematics: Graphs, Slope, and Area under Curves

Vocabulary flashcards covering slope and area concepts in kinematic graphs (displacement, velocity, acceleration).

Displacement

The total change in position; in kinematics it is represented by the cumulative area under a velocity–time graph from the start time to time t.

Velocity

Rate of change of displacement; the slope of a displacement–time graph.

Acceleration

Rate of change of velocity; the slope of a velocity–time graph.

Slope

In kinematic graphs: the slope of a displacement–time graph equals velocity; the slope of a velocity–time graph equals acceleration.

Area Under the Curve

The signed area between a curve and the time axis over a given interval; on velocity–time graphs it yields displacement; on acceleration–time graphs it yields velocity.

Cumulative Area

The total accumulated area from the start up to a given time; sum of areas from all previous time intervals.

Negative Area

Area that lies below the time axis; contributes a negative value to the cumulative total.

Velocity-Time Graph

A graph of velocity versus time; its area equals displacement and its slope equals acceleration.

Acceleration-Time Graph

A graph of acceleration versus time; its area equals velocity.

Displacement-Time Graph

A graph of position versus time; its slope gives velocity.

Rectangle Area (in area calculations)

A rectangular portion used to estimate or sum areas under a velocity- or acceleration-time curve.

Triangle Area (in area calculations)

A triangular portion used to estimate or sum areas under a velocity- or acceleration-time curve.