Glossary
Acceleration Vector
A vector that describes the rate at which an object's velocity is changing, indicating changes in speed, direction, or both.
Example:
When a roller coaster speeds up going down a hill, its acceleration vector points in the direction of increasing speed.
Average Rate of Change
The ratio of the change in a function's output to the change in its input over a given interval, calculated independently for x(t) and y(t) in parametric functions.
Example:
Calculating the average rate of change of a stock price over a week tells you its average daily gain or loss during that period.
Parametric Functions
Functions where the x and y coordinates of a point are each expressed in terms of a third independent variable, typically 't' (time), allowing for the description of motion along a curve.
Example:
Describing the path of a baseball thrown through the air, where its horizontal position x(t) and vertical position y(t) both depend on time t.
Particle at Rest
A condition where a particle's velocity vector is zero, meaning both its x-component and y-component of velocity are simultaneously zero.
Example:
A particle at rest on a graph would show no change in its x or y position over time, like a ball momentarily stopped at the peak of its bounce.
Position Vector
A vector that specifies the location of a point or object in space relative to an origin at a given time.
Example:
For a drone flying, its position vector at any moment tells you exactly where it is in the sky relative to its starting point.
Slope of the Graph (Parametric)
The instantaneous rate of change of y with respect to x for a parametric curve, found by dividing the rate of change of y with respect to t by the rate of change of x with respect to t (dy/dt / dx/dt).
Example:
Finding the slope of the graph of a projectile's path at its peak tells you the exact steepness of its trajectory at that moment.
Speed (of a particle)
The magnitude of the velocity vector, representing how fast an object is moving without regard to its direction.
Example:
If a car's velocity vector is <30, 40> mph, its speed is 50 mph, calculated as the hypotenuse of the velocity components.
Velocity Vector
A vector that indicates both the instantaneous speed and the direction of an object's motion at a specific moment in time.
Example:
If a car is moving at 60 mph northeast, its velocity vector would point northeast with a magnitude representing 60 mph.
X-Component of Motion
The horizontal part of an object's movement, described by the x(t) parametric equation, indicating left-right movement.
Example:
If a robot moves right when x(t) is increasing, its x-component of motion is positive.
Y-Component of Motion
The vertical part of an object's movement, described by the y(t) parametric equation, indicating upward-downward movement.
Example:
When a hot air balloon ascends, its y-component of motion is positive, indicating upward movement.