The motion of objects is often understood best by constructing distance time graphs. These graphs look at the distance an object travels over time. On a distance time graph, the time is the independent variable and is placed on the "x" axis. The distance traveled is the dependent variable. It is placed on the "y" axis.

Here are some examples of distance time graphs.

Graph A

Graph A: This distance time graph is for an object at rest. We know it is at rest because the distance does not change during the 4s time period between 1s and 5s.

Graph B

Graph B: This is a distance time graph of an object with a constant velocity. Note that it appears as a diagonal line. There is an equal change in distance during each 1second time interval. One easy way to determine that this is a constant velocity is to calculate the velocity for several data points. For instance at 1s the distance traveled was 3m. Calculating using the velocity equation: v=d/t, v=3m/1.0s, **v=3m/s. **If we calculate the velocity for other times we get the same answer, 3.0m/s! The velocity is constant.

Graph C: This is a **distance time** graph of an object that has a **constant acceleration. **Note that the distance changes as a square of the time. this is why the distance time graph shows the characteristic parabolic curve. Every second of motion the object travels further than it did in the previous escond.

Graph C

Graph D

Graph D: This is a graph showing how the velocity changes over time for an accelerating object. During the time period from 1s up to 3s the velocity of the object was 10km/h. During the one second interval between 3s and 4s the object came to a rest at 0km/h. Between 6s and 7s the object accelerated up to 6km/h. The object's velocity was constant at 6km/h until 11s. Between 11s and 14s the object accelerated up to a maximum velocity of 20m/s.

The acceleration of the object in graph "D" can be determined for any segment of the graph. During the last 3 seconds shown in graph "D", the object accelerates from 6m/s to 20m/s. From this we can determine that the acceleration during this time is: