Rates of Change and Distance-Time Graphs

A set of vocabulary flashcards reviewing gradients, positive/negative/zero rates of change, linear and curved relationships, and distance-time graph motions.

Rate of change

The gradient of a curve that indicates how quickly the value of $y$ is changing.

Speed

The rate of change of distance over time, which can also be considered as a gradient on a distance-time graph.

Constant rate of change

A characteristic of straight lines where there is a fixed change in $y$ for each unit increase in $x$, resulting in a constant gradient.

Varying rate of change

A characteristic of curved graphs where the change in $y$ varies for each unit increase in $x$, meaning the gradient varies depending on the point on the curve.

Positive rate of change

A gradient that occurs when $y$ increases as $x$ increases.

Negative rate of change

A gradient that occurs when $y$ decreases as $x$ increases.

Zero rate of change

A gradient that occurs when $y$ does not change as $x$ increases.

Distance-time graph

A graph that models a journey over time, where distance from a reference point (such as home, where $\text{distance} = 0$) is plotted against time.

Decelerating away from home

A distance-time journey where distance from home is increasing at a decreasing rate.

Accelerating away from home

A distance-time journey where distance from home is increasing at an increasing rate.

Accelerating towards home

A distance-time journey where distance from home is decreasing at an increasing rate.

Decelerating towards home

A distance-time journey where distance from home is decreasing at a decreasing rate.