First let us know the importance of Distance-Time Graph: We deal with 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 rectangular graph, we will obtain distance – time graph corresponding to the motion of that body.
Suppose a bus driver is driving at a constant speed which is indicated by the speedometer and the driver measures the time taken by the bus for every kilometer. The driver notices that the bus travels 1 kilometer in every 2 minutes. He prepares the data table after this so that he has a clear understanding for 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.
The following things can be concluded now:
- If distance time graph is a straight line then the motion is uniform.
- If distance time graph of any body is given, its speed can be calculated using the slope of the graph.
- The slope of the straight line graph is 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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