## What is a Distance-Time Graph?

A distance-time graph shows how far an object has travelled in a given time. It is a simple line graph that denotes distance versus time findings on the graph.

- Distance is plotted on the Y-axis.
- Time is plotted on the X-axis.

**Note:** *Curved lines on a distance-time graph indicate that the speed is changing.*

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## Importance of Distance-Time Graph

We deal with the distance-time graph while studying the motion of bodies. If we record distance and time for the motion of a body and plot the same data on a rectangular graph, we will obtain a distance-time graph corresponding to the motion of that body.

### Example:

For better understanding, let us consider an example of uniform motion. A bus driver drives at a constant speed which is indicated by the speedometer and the driver measures the time taken by the bus for every kilometre. The driver notices that the bus travels 1 kilometre in every 2 minutes.

*He prepares the data table after this so that he has a clear understanding of everything and then draws the graph as shown below.*

By this table, he had a clear idea about the speed which is: ½ × 60 = **30 km/hr**.

The graph is a straight line and the motion of the bus is also uniform. Also, from the graph, we can find the speed of the bus at any instant of time. The initial and final position of the car can be found as the following:

**Speed** = (Final Position-Initial position)/Time

The slope of the line can be found by drawing a rectangle anywhere near the straight line which determines the speed of the bus. If an object is not moving, the distance-time graph results in a horizontal line which shows that the object is at rest.

## Conclusion:

*The following things can be concluded now:*

- If the distance-time graph is a straight line then the motion is uniform.
- If the distance-time graph of anybody is given, its speed can be calculated using the slope of the graph.
- The slope of the straight-line graph is the same irrespective of the interval which is chosen. This implies that the speed of an object under uniform motion remains constant.

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