Distance-Time and Velocity-Time Graphs

What are distance-time and velocity-time graphs?

In this post, we interpret the meaning of the gradient of a function in a variety of contexts, for example on distance–time or velocity-time graphs, as a part of the Prelim Maths Advanced course under the topic Calculus and sub-part Difference Quotients.

A distance-time graph is a graph with distance on the $y$ -axis and time on the $x$ -axis, while a velocity-time graph is a graph with velocity on the $y$ -axis and time on the $x$ -axis. These graphs are important, as the rate of change of the distance-time graph represents the points on the velocity-time graph, as: $velocity = \frac{distance}{time}$ .

How do I read distance-time and velocity-time graphs?

The following two videos give us insight into the nature of distance-time and velocity-time graphs and how we are able to utilise these graphs to take information out and solve problems.