How to use **graph paper to draw motion graphs**? – Plotting motion graphs is important if we want to learn motion physics well. In this tutorial, we will find out how to use a common graph paper to draw the motion graphs. For this, we will start by knowing what a graph is.

## What is a graph?

This is a two-dimensional diagram. It can be portrayed using two quantities. A graph has two axes. The horizontal axis is the ‘X’ axis and the vertical, ‘Y’ axis. The point ‘O’ is the origin. This is where X and Y axes meet. The axis towards the right from the origin is taken as the positive X-axis (OX) and to the left as the negative X-axis (OX’). In a similar way, OY and OY’ are considered as positive and negative axes.

## How to use a graph to draw a position-time graph?

We can find out equations connecting the quantities represented by X and Y. Values obtained by these equations can be marked in a graph. Similarly, we can find out the values of the other equations using this graph.

Draw on a graph paper the axes X’OX and Y’OY.

Mark the values given in Table 1 on this graph. Join the markings. What is the nature of the graph obtained?

Time (s) on X-axis | 0 | 2 | 4 | 6 | 8 | 10 |

Position (m) on Y-axis | 0 | 10 | 20 | 30 | 40 | 50 |

**Table 1: data set to draw a position – time graph**

The graph has position along Y-axis and time along the X-axis. Now you need to plot each time-position pair data on the graph and connect those makings. You will get the time-position graph (a motion graph) as shown below.

## How can we find the position of an object at a particular time from a position-time graph?

The position-time graph of a car is given. Let’s see how to find out from the graph the distance traveled by car in 8 seconds.

First, let’s find the position of an object at a particular time from a position-time graph (here 8th second).

– Draw a perpendicular from the X-axis to the position-time graph at the eighth second.

– From the point where the perpendicular meets the graph, draw another perpendicular to the Y-axis. The point at which this perpendicular meets the Y-axis is the distance traveled by car in 8 s.

As per diagram 2 above, the value is 40 m.

## How to draw the speed-time graph of a moving object from a set of data?

Let’s draw a speed-time graph from the data in the table below. A speed-time graph can be drawn by taking, on a convenient scale, time on X-axis and speed on Y-axis.

Time(s) on X-axis | 0 | 2 | 4 | 6 | 8 | 10 |

Speed (m/s) on Y-axis | 0 | 2 | 6 | 8 | 6 | 10 |

**Table 2: data set to draw a speed – time graph**

Here is the speed-time graph according to the given data set.

## How to draw the velocity-time graph of a moving object from a set of data?

A velocity-time graph can be drawn by taking, on a convenient scale, time on X-axis and velocity on Y-axis. Let’s consider the table below for the velocity and time data sets.

Time(s) on X-axis | 0 | 1 | 2 | 3 | 4 | 5 |

Velocity (m/s) on Y-axis | 0 | 1 | 2 | 3 | 4 | 5 |

**Table 3: data set to draw a velocity – time graph**

## Take Away

Here we have seen how a common graph paper is used to draw motion graphs like the position-time graph, speed-time graph, and velocity-time graph when a set of corresponding data is available.