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# 13. Time and Motion

In Class VI, you learnt about different types of motions. You learnt that a motion could be along a straight line, it could be circular or periodic. Can you recall these three types of motions?

Table 13.1 gives some common examples of motions. Identify the type of motion in each case.

**Table 13.1** Some examples of different types of motion

It is common experience that the motion of some objects is slow while that of some others is fast.

## 13.1 SLOW OR FAST

We know that some vehicles move faster than others. Even the same vehicle may move faster or slower at different times. Make a list of ten objects moving along a straight path. Group the motion of these objects as slow and fast. How did you decide which object is moving slow and which one is moving fast.

If vehicles are moving on a road in the same direction, we can easily tell which one of them is moving faster than the other.

## 13.2 SPEED

You are probably familiar with the word speed. In the examples given above, a higher speed seems to indicate that a given distance has been covered in a shorter time, or a larger distance covered in a given time.

The most convenient way to find out which of the two or more objects is moving faster is to compare the distances moved by them in a unit time.
Thus, if we know the distance covered by two buses in one hour, we can tell which one is slower. We call the distance covered by an object in a unit time as the **speed** of the object.

When we say that a car is moving with a speed of 50 kilometers per hour, it implies that it will cover a distance of 50 kilometers in one hour. However, a car seldom moves with a constant speed for one hour. In fact, it starts moving slowly and then picks up speed. So, when we say that the car has a speed of 50 kilometers per hour, we usually consider only the total distance covered by it in one hour. We do not bother whether the car has been moving with a constant speed or not during that hour. The speed calculated here is actually the average speed of the car. In this book **we shall use the term speed for average speed. So, for us the speed is the total distance covered divided by the total time taken.** Thus,

In everyday life we seldom find objects moving with a constant speed over long distances or for long durations of time. If the speed of an object moving along a straight line keeps changing, its motion is said to be ** non-uniform** . On the other hand, an object moving along a straight line with a constant speed is said to be in ** uniform motion** . In this case, the average speed is the same as the actual speed.

We can determine the speed of a given object once we can measure the time taken by it to cover a certain distance. You have already learnt how to measure distances. But, how do we measure time? Let us find out.

## 13.3 MEASUREMENT OF TIME

If you did not have a clock, how would you decide what time of the day it is? Have you ever wondered how our elders could tell the approximate time of the day by just looking at shadows?

How do we measure time interval of a month? A year?

Our ancestors noticed that many events in nature repeat themselves after
definite intervals of time. For example, they found that the sun rises everyday
in the morning. The time between one sunrise and the next was called a day.
Similarly, a month was measured from one new moon to the next. A year was
fixed as the time taken by the earth to complete one revolution of the sun.

Often we need to measure intervals of time which are much shorter than a day. Clocks or watches are perhaps the most common time measuring devices. Have you ever wondered how clocks and watches measure time?

The working of clocks is rather complex. But all of them make use of
some periodic motion. One of the most well-known periodic motions is that of
a **simple pendulum.**

(a) Wall clock

**and**(b) Table clock

(c) Digital clock

**Fig. 13.3**Some common clocks

Fig. 13.4 (a) A simple pendulum Fig. 13.4 (b) Different positions of the bob of an oscillating simple pendulum

A simple pendulum consists of a small metallic ball or a piece of stone
suspended from a rigid stand by a thread [Fig. 13.4 (a)]. The metallic ball
is called the ** bob** of the pendulum.

Fig. 13.4 (a) shows the pendulum at rest in its mean position. When the bob
of the pendulum is released after taking it slightly to one side, it begins to move
to and fro [Fig. 13.4 (b)]. The to and fro motion of a simple pendulum is an
example of a periodic or an ** oscillatory** motion.

The pendulum is said to have completed one ** oscillation** when its bob,starting from its mean position O, moves to A, to B and back to O. The pendulum also completes one oscillation when its bob moves from one extreme position A to the other extreme position B and comes back to A. The time taken by the pendulum to complete one oscillation is called its** time period**.

**Units of time and speed **

The basic unit of time is a **second**. Its symbol is s. Larger units of time are
minutes (min) and hours (h). You already know how these units are related
to one another.

What would be the basic unit of speed?

Since the speed is distance/time, the basic unit of speed is m/s. Of course, it could also be expressed in other units such as m/min or km/h.

You must remember that **the symbols of all units are written in
singular**. For example, we write 50 km and not 50 kms, or 8 cm and not 8 cms.

Boojho is wondering how many seconds there are in a day and how many hours in a year. Can you help him?

There is an interesting story about the discovery that the time period of a givenpendulum is constant. You might have heard the name of famous scientist Galileo Galilie (A.D. 1564 –1642). It is said that once Galileo was sitting in a church. He noticed that a lamp suspended from the ceiling with a chain was moving slowly from one side to the other. He was surprised to find that his pulse beat the same number of times during the interval in which the lamp completed one oscillation. Galileo experimented with various pendulums to verify his observation. He found that a pendulum of a given length takes always the same time to complete one oscillation. This observation led to the development of pendulum clocks. Winding clocks and wristwatches were refinements of the pendulum clocks.

Different units of time are used depending on the need. For example, it is convenient to express your age in years rather than in days or hours. Similarly, it will not be wise to express in years the time taken by you to cover the distance between your home and your school.

How small or large is a time interval of one second? The time taken in saying aloud “two thousand and one” is nearby one second. Verify it by counting aloud from "two thousand and one" to "two thousand and ten". The pulse of a normal healthy adult at rest beats about 72 times in a minute that is about 12 times in 10 seconds. This rate may be slightly higher for children.

Paheli wondered how time was measured when pendulum clocks were not available.

Many time measuring devices were used in different parts of the world before the pendulum clocks became popular. Sundials, water clocks and sand clocks are some examples of such devices. Different designs of these devices were developed in different parts of the world (Fig. 13.5).

## 13.4 MEASURING SPEED

Having learnt how to measure time and distance, you can calculate the speed of an object. Let us find the speed of a ball moving along the ground.

The smallest time interval that can be measured with commonly available clocks and watches is one second. However, now special clocks are available that can measure time intervals smaller than a second. Some of these clocks can measure time intervals as small as one millionth or even one billionth of a second. You might have heard the terms like microsecond and nanosecond. One microsecond is one millionth of a second. A nanosecond is one billionth of a second. Clocks that measure such small time intervals are used for scientific research. The time measuring devices used in sports can measure time intervals that are one tenth or one hundredth of a second. On the other hand, times of historical events are stated in terms of centuries or millenniums. The ages of stars and planet are often expressed in billions of years. Can you imagine the range of time intervals that we have to deal with?

(a) Sundial at Jantar Mantar, Delhi

(b) Sand clock and (c) Water clock

**Fig. 13.5**Some ancient time-measuring devices

Fig. 13.6 Measuring the speed of a ball

Measure the distance between the point at which the ball crosses the line and the point where it comes to rest. You can use a scale or a measuring tape. Let different groups repeat the activity. Record the measurements in Table 13.3. In each case calculate the speed of the ball.

You may now like to compare your speed of walking or cycling with that of your friends. You need to know the distance of the school from your home or from some other point. Each one of you can then measure the time taken to cover that distance and calculate your speed. It may be interesting to know who amongst you is the fastest. Speeds of some living organisms are given in

**Table 13.3 Distance moved and time taken by a moving ball**

Name of the group | Distance moved by the ball (m) | Time taken (s) | Speed = Distance/Time taken (m/s) |
---|---|---|---|

Table 13.4, in km/h. You can calculate the speeds in m/s yourself.

Rockets, launching satellites into earth’s orbit, often attain speeds up to 8 km/s. On the other hand, a tortoise can move only with a speed of about 8 cm/s. Can you calculate how fast is the rocket compared with the tortoise?

Once you know the speed of an object, you can find the distance moved by it in a given time. All you have to do is to multiply the speed by time. Thus,

Distance covered = Speed x Time

You can also find the time an object would take to cover a distance while moving with a given speed.

Time taken = Distance/Speed

Boojho wants to know whether there is any device that measures the speed.

You might have seen a meter fitted on top of a scooter or a motorcycle.
Similarly, meters can be seen on the dashboards of cars, buses and other
vehicles. Fig. 13.7 shows the dashboard of a car. Note that one of the meters has km/h written at one corner. This is called a **speedometer**. It records the

**Table 13.4 Fastest speed that some animals can attain**

S. No. | Name of the object | Speed in km/h | Speed in m/s |
---|---|---|---|

1. | Falcon | 320 | |

2. | Cheetah | 112 | |

3. | Blue fish | 40 – 46 | |

4. | Rabbit | 56 | |

5. | Squirrel | 19 | |

6. | Domestic mouse | 11 | |

7. | Human | 40 | |

8. | Giant tortoise | 0.27 | |

9. | Snail | 0.05 |

**Fig. 13.7**The dashboard of a car

speed directly in km/h. There is also another meter that measures the
distance moved by the vehicle. This meter is known as an **odometer**.

While going for a school picnic, Paheli decided to note the reading on the odometer of the bus after every 30 minutes till the end of the journey.

Later on she recorded her readings in Table 13.5.

Can you tell how far was the picnic spot from the school? Can you calculate the speed of the bus? Looking at the Table, Boojho teased Paheli whether she can tell how far they would have travelled till 9:45 AM. Paheli had no answer to this question. They went to their teacher. She told them that one way to solve this problem is to plot a distance-time graph. Let us find out how such a graph is plotted.

## 13.5 DISTANCE-TIME GRAPH

You might have seen that newspapers, magazines, etc., present information in various forms of graphs to make it

**Table 13.5 Odometer reading at different times of the journey**

Time (AM) | Odometer reading | Distance from the starting point |
---|---|---|

8:00 AM | 36540 km | 0 km |

8:30 AM | 36560 km | 20 km |

9:00 AM | 36580 km | 40 km |

9:30 AM | 36600 km | 60 km |

10:00 AM | 36620 km | 80 km |

**Fig. 13.8**A bar graph showing runs scored by a team in each over

interesting. The type of graph shown in Fig. 13.8 is known as a bar graph. Another type of graphical representation is a pie chart (Fig. 13.9). The graph shown in Fig. 13.10 is an example of a line graph. The distance-time graph is a line graph. Let us learn to make such a graph.

**Fig. 13.9**A pie chart showing composition of air

**Fig. 13.10**A line graph showing change in weight of a man with age

Take a sheet of graph paper. Draw two lines perpendicular to each other on it, as shown in Fig. 13.11. Mark the horizontal line as XOX'. It is known as the x-axis. Similarly mark the vertical line YOY'. It is called the y-axis. The point of intersection of XOX' and YOY' is known as the origin O. The two quantities between which the graph is drawn are shown along these two axes. We show the positive values on the x-axis along OX. Similarly, positive values on the y-axis are shown along OY. In this chapter we shall consider only the positive values of quantities.

**Fig. 13.11**x-axis and y-axis on a graph paper

Therefore, we shall use only the shaded part of the graph shown in Fig. 13.11.

Boojho and Paheli found out the distance travelled by a car and the time taken by it to cover that distance. Their data is shown in Table 13.6.

**Table 13.6 The motion of a car**

S. No. | Time | Distance |
---|---|---|

1 | 0 | 0 |

2 | 1 min | 1 km |

3 | 2 min | 2 km |

4 | 3 min | 3 km |

5 | 4 min | 4 km |

6 | 5 min | 5 km |

- You can make the graph by following the steps given below:
- Draw two perpendicular lines to represent the two axes and mark them as OX and OY as in Fig. 13.11
- Decide the quantity to be shown along the x-axis and that to be shown along the y-axis. In this case we show the time along the x-axis and the distance along the y-axis.
- Choose a scale to represent the distance and another to represent the time on the graph. For the motion of the car scales could be
Time: 1 min = 1 cm

Distance: 1 km = 1 cm

- 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 min, 2 min, … on the x-axis from the origin O. Similarly, mark the distance 1 km, 2 km … on the y-axis (Fig. 13.12).
- Now you have to mark the points on the graph paper to represent each
set of values for distance and time. Observation recorded at S. No. 1 in Table 13.6 shows that at time 0 min the distance moved is also
zero. The point corresponding to this set of values on the graph will
therefore be the origin itself. After 1 minute, the car has moved a distance
of 1 km. To mark this set of values look for the point that represents
1 minute on the x-axis. Draw a line parallel to the y-axis at this point.
Then draw a line parallel to the x-axis from the point corresponding
to distance 1 km on the y-axis. The point where these two lines
intersect represents this set of values on the graph (Fig. 13.12). Similarly, mark on the graph paper the points corresponding to different
sets of values.
**Fig. 13.12**Making a graph**Fig. 13.13**Making a graph - Fig. 13.13 shows the set of points on the graph corresponding to positions of the car at various times.
- Join all the points on the graph as shown in Fig. 13.13. It is a straight line. This is the distance-time graph for the motion of the car.
- If the distance-time graph is a straight line, it indicates that the object is moving with a constant speed. However, if the speed of the object keeps changing, the graph can be of any shape.
**Fig. 13.14**Distance-time graph of the bus - the difference between the highest and the lowest values of each quantity.
- the intermediate values of each quantity, so that with the scale chosen it is convenient to mark the values on the graph, and
- to utilise the maximum part of the paper on which the graph is to be drawn.

Generally, the choice of scales is not as simple as in the example given above. We may have to choose two different scales to represent the desired quantities on the x-axis and the y-axis. Let us try to understand this process with an example.

Let us again consider the motion of the bus that took Paheli and her friends to the picnic. The distance covered and time taken by the bus are shown in Table 13.5. The total distance covered by the bus is 80 km. If we decide to choose a scale 1 km = 1 cm, we shall have to draw an axis of length 80 cm. This is not possible on a sheet of paper. On the other hand, a scale 10 km = 1 cm would require an axis of length only 8 cm. This scale is quite convenient. However, the graph may cover only a small part of the graph paper. Some of the points to be kept in mind while choosing the most suitable scale for drawing a graph are:

Suppose that we have a graph paper of size 25 cm x 25 cm. One of the scales which meets the above conditions and can accommodate the data of Table 13.5 could be

Distance: 5 km = 1 cm, and

Time: 6 min = 1 cm

Can you now draw the distance-time graph for the motion of the bus? Is the graph drawn by you similar to that shown in Fig. 13.13?

Distance-time graphs provide a variety of information about the motion when compared to the data presented by a table. For example, Table 13.5 gives information about the distance moved by the bus only at some definite time intervals. On the other hand, from the distance-time graph we can find the distance moved by the bus at any instant of time. Suppose we want to know how much distance the bus had travelled at 8:15 AM. We mark the point corresponding to the time (8:15 AM) on the x-axis. Suppose this point is A. Next we draw a line perpendicular to the x-axis (or parallel to the y-axis) at point A. We then mark the point, T, on the graph at which this perpendicular line intersects it (Fig. 13.14). Next, we draw a line through the point T parallel to the x-axis. This intersects the y-axis at the point B. The distance corresponding to the point B on the y-axis, OB, gives us the distance in km covered by the bus at 8:15 AM. How much is this distance in km? Can you now help Paheli to find the distance moved by the bus at 9:45 AM? Can you also find the speed of the bus from its distance-time graph?

- Bar graph
- Graphs
- Non-uniform motion
- Oscillation
- Simple pendulum
- Speed
- Time period
- Uniform motion
- Unit of time