NCERT Book Class 9 Science Lab Manual Moving Things People and Ideas

Moving Things, People and Ideas

AIM

To plot distance – time (s – t ) graph for an object moving with a uniform speed from a given set of s and t data and to determine the speed of the object.

THEORY

A moving object changes its position with time. If the object travels a distance s in time t then its speed is

                          v = s/t

When an object travels equal distances in equal intervals of time, it is said to have a uniform speed. But if the speed or its direction of motion changes with time then the object is said to be in nonuniform motion.

For a uniform motion the distance travelled by the object is directly proportional to time taken. Thus the graph of distance travelled against time is a straight line. This distance-time graph can be used to determine the speed of the object. Fig. 32.1 shows the distance–time (s – t) graph of an object moving with uniform speed. To find the speed of the object consider a small part AB of the s – t graph. The two lines PAC and BCQ drawn parallel to x-axis and y-axis respectively, meet each other at point C to form a triangle ABC. The segment AC denotes the time interval (t₂ – t₁) while the segment BC corresponds to the distance (s₂ – s₁). From this graph it can be seen that as the object moves from the point A to point B, it covers a distance (s₂ – s₁) in time (t₂ – t₁). The speed, v of the object, therefore can be represented as

                                    v = s₂-s₁/t₂-t₁ = BC/AC

This is also the slope of s – t graph. Larger the slope of the graph more is the speed of the object. The s – t graph can also be used to estimate the speed of the object even at the times not given in the data. One can estimate these values at a time within the range of the given time interval at which the position of the object is not given in the given data (interpolation). One can similarly use the graph to obtain the values of object position and speed at a time beyond the given range of data (extrapolation). On the other hand, Eq. (1) can only be used to determine the speed at instants for which the distance is given in the data.

MATERIALS REQUIRED

Graph paper

PROCEDURE

1. Examine the given data of distance (s) of the object at different times (t ). Find the difference between the highest and the lowest values of each quantity (these are the ranges of the distance and time values.) Table 1 shows the data for the distance travelled by a car (in m) and the time taken (in s) by it to cover that distance. In this table the time values range from 0 to 10 s while the distance values range between 0 and 100 m.

2. Take a graph paper and draw two perpendicular lines OX and OY to represent x-axis and y-axis, respectively (Fig. 32.1). Measure the lengths (or count the number of divisions available) on the graph paper along the two axes. Let, for example, the graph paper you have been provided is 15 cm (or 15 cm divisions) along the x-axis and 25 cm (or 25 cm divisions) along the y-axis.) 

3. Decide the quantity to be shown along the x-axis and that to be shown along the y-axis. Conventionally, time is shown along the x-axis and the distance along the y-axis.

4. On the basis of available divisions on the two axes and ranges of the given distance and time data, choose a scale to represent the distance along the y-axis and another scale to represent the time along the x-axis. For example, the scales for the motion of the car as given in Table 1, could be time 1 s = 1 cm; and distance 10 m = 2 cm. (Try to utilise the maximum part of the graph paper while choosing the scales.)

5. Mark values for the time and the distance on the respective axes according to the scale you have chosen. For the motion of the car, mark the time 1 s, 2 s, 3 s … on the x-axis at every cm from the origin O. Similarly, mark the distance 10 m, 20 m, 30 m ... on the y-axis at every 2 cm from the origin .

6. Now mark the points on the graph paper to represent each set of values for distance and time given in the data provided.

7. Join all the marked points on the graph paper. This is the plotting of s – t graph of the data provided for the motion of a car. Check if this graph is a straight line. A straight line graph indicates that the car is moving with a constant speed.

OBSERVATIONS AND CALCULATIONS

To find the speed of the car, take any two points on the straight line graph and find their corresponding values of t and s (as suggested in the theory part above). For convenience it is suggested to take the points that correspond to integral values of time and distance values. Suppose the coordinates of these two points are (t₁, s₁,) and (t₂, s₂). The distance travelled by the car in time interval (t₂ – t₁) is (s₂ – s₁). Calculate the speed of the car during this time interval (t₂ – t₁) using Eq. (2).

Please refer to attached file for NCERT Class 9 Science Lab Manual Moving Things People and Ideas