# Displacement-Time Graphs

Displacement-time graphs show an object’s position relative to its starting point over a period of time. They’re useful because they can be used to describe an object’s motion as well as find its velocity at a given point.

## Plotting displacement-time graphs

Let’s see how to plot displacement-time graphs for moving objects.

The suvat equations can be used to work out values to plot.

Displacement is plotted on the y-axis and time on the x-axis.

Let’s solve a problem to understand the procedure of plotting a displacement-time graph.

**Plot a displacement-time graph for a panther who accelerates constantly from rest at 2.0 ms ^{–2} for 5.0 seconds.**

**Solution:**

Known values:

**Acceleration = a = 2 ms ^{–2}**

**Initial velocity = u = 0**

To find the displacement, we will use this *suvat equation*: s = ut + (1/2)at^{2}

Here, u =0.

Hence, we can write: s = (1/2)at^{2} ………. (1)

Here, s = (1/2) 2. t^{2} = t^{2}

Now pick values of t between 0 and 5.0 seconds

and work out the values of s at those points with s = t^{2}: …then plot the graph:

Displacement is plotted on the y-axis and time on the x-axis.