Theory:

In all the cases, the scale value may not be the same to plot a graph. Two different scales have to be chosen for the quantities on \(x\)-axis and \(y\)-axis, depending on the given data.
  
Motion of a bus
 
Here, the motion of a bus is taken as an example to plot a distance-time graph.
 
bus-2506652_1280.jpg
 
The time and the distance travelled by the bus is given in the following table.
 
Time
(\(AM\))
Odometer reading
(\(km\))
Distance
(\(km\))
 
\(8\) \(:\) \(00\)
\(36500\)
\(0\)
\(8\) \(:\) \(30\)
\(36520\)
\(20\)
\(9\) \(:\) \(00\)
\(36540\)
\(40\)
\(9\) \(:\) \(30\)
\(36560\)
\(60\)
\(10\) \(:\) \(00\)
\(36580\)
\(80\)
 
The total distance covered by the bus is \(80\ km\). If a scale is chosen as \(1\ km\) \(=\) \(1\ cm\), then an axis of length \(80\ cm\) should be drawn. But it is not possible to draw in a sheet of paper. So, a scale of \(10\ km\) \(=\) \(1\ cm\) can be used to show an axis of length \(8\ cm\) which is possible to draw in a paper. But, this graph covers only a small part of the graph.
  
Certain points to choose a suitable scale for drawing a graph:
  • the difference between the highest and the lowest values of a quantity.
  • the intermediate values of each given quantity, and
  • the utilisation of the maximum part of the paper.
Keeping these points in mind, a distance-time graph can be drawn with any value of scale.
 
g3.jpg
  1. To find the distance covered by a bus at \(8\) \(:\) \(15\) \(AM\), a point (\(A\)) is marked corresponding to the time on the \(x\)-axis.
  2. A perpendicular line (\(T\)) is drawn to the \(x\)-axis at \(A\) so that they intersect each other.
  3. A line parallel to the \(x\)-axis intersects the \(y\)-axis at the point (\(B\)) is drawn through \(T\).
  4. Thus, the line \(OB\) gives the distance covered by the bus at \(8\) \(:\) \(15\) \(AM\).
Shapes of graph:
 
shutterstock_1718229304 (1).jpg
  
The straight line in the distance-time graph represents that the object is in uniform motion. If the line is not uniform (curvy or irregular), then the object is in non-uniform motion.
  
Advantages of the distance-time graph
  1. It provides information about the motion of any object, i.e., the distance moved at a definite time interval.
  2. It helps to find the distance covered at any specific time interval.