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.
The time and the distance travelled by the bus is given in the following table.
\(8\) \(:\) \(00\)
\(8\) \(:\) \(30\)
\(9\) \(:\) \(00\)
\(9\) \(:\) \(30\)
\(10\) \(:\) \(00\)
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.
- 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.
- A perpendicular line (\(T\)) is drawn to the \(x\)-axis at \(A\) so that they intersect each other.
- A line parallel to the \(x\)-axis intersects the \(y\)-axis at the point (\(B\)) is drawn through \(T\).
- Thus, the line \(OB\) gives the distance covered by the bus at \(8\) \(:\) \(15\) \(AM\).
Shapes of graph:
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
- It provides information about the motion of any object, i.e., the distance moved at a definite time interval.
- It helps to find the distance covered at any specific time interval.