Kinematics and Graphing Review

Vocabulary flashcards covering one-dimensional kinematics, kinematic equations, and the interpretation of position-time, velocity-time, and acceleration-time graphs.

Kinematic Equations

A system of equations for motion with constant acceleration, consisting of: $d = v_i t + \frac{1}{2} a t^2$, $v_f = v_i + a t$, $v_f^2 = v_i^2 + 2 a d$, and $d = \frac{v_i + v_f}{2} t$.

Position-Time Graph

A graph that shows where an object is located over a period of time, whose slope indicates how fast the object is moving (velocity) and whose sign indicates the direction of motion.

Slope of a Position-Time Graph

The numerical value indicating velocity; a steeper line indicates a faster-moving object, while a horizontal line with a slope of $0$ indicates an object at rest.

Velocity-Time Graph

A graph representing velocity over time, where values located above the time axis indicate positive velocity, values below indicate negative velocity, and the slope represents acceleration.

Area Under the Curve

The region bounded by a velocity-time graph line and the time axis, which represents the total displacement of the moving object.

Speeding Up

The condition where the line on a velocity-time graph moves away from the time axis ($0\,\text{m/s}$) and the acceleration vector points in the same direction as the velocity vector.

Slowing Down

The condition where the line on a velocity-time graph moves toward the time axis ($0\,\text{m/s}$), corresponding to a flattening slope on a position-time graph.

Direction Change on a Position-Time Graph

The turning point where the slope of the position-time curve reverses sign, having an instantaneous slope of $0$ at the peak or trough.

Direction Change on a Velocity-Time Graph

The moment an object's motion changes direction, occurring where the graph crosses the time axis ($v = 0\,\text{m/s}$).

Constant Acceleration on an Acceleration-Time Graph

A horizontal line with zero slope, showing that acceleration remains uniform and unchanged over time.

Freely Rolling Cart Acceleration (Cart on a Ramp Lab)

The constant acceleration value that remains identical whether the cart is at the bottom, middle, or top of the ramp while rolling freely.

Zero Acceleration

A state of motion occurring during time intervals where the velocity-time graph is horizontal (zero slope), meaning velocity is constant.