Question

You have a motion graph for an object that shows distance and time. How does the slope of the graph relate to the object's speed?

Answer 1

The slope of a graph is given by
`(\Delta y)/(\Delta x)`, or in English, the change in y divided by the change in x.

In the case of a distance-time graph, assuming distance is plotted on the y-axis and time on the x-axis, the slope would equal the change in distance divided by the change in time.


`\frac{\text{distance}}{\text{time}} = \text{speed}`

So, speed is represented by the slope.

Another way of looking at this (and confirming it if you're ever unsure with a similar question) is by using dimensional analysis, which is a fancy way of saying 'look at the units'.

Distance is measured in metres (m), and time in seconds (s). The slope therefore would be equal to

`(m)/(s) = ms^(-1) = \text{the unit of speed.}`