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.

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.

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:

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.