Motion and Time PDF

9 Motion and Time I n Class VI, you learnt about different 9.1 SLOW OR FAST types of motions. You learnt that a We know that some vehicles move faster motion could be along a straight line, than others. Even the same vehicle may it could be circular o...

9 Motion and Time I n Class VI, you learnt about different 9.1 SLOW OR FAST types of motions. You learnt that a We know that some vehicles move faster motion could be along a straight line, than others. Even the same vehicle may it could be circular or periodic. Can you move faster or slower at different times. recall these three types of motions? Make a list of ten objects moving along Table 9.1 gives some common a straight path. Group the motion of examples of motions. Identify the type these objects as slow and fast. How did of motion in each case. you decide which object is moving slow Table 9.1 Some examples of and which one is moving fast? different types of motion If vehicles are moving on a road in Example of Type of motion the same direction, we can easily tell which one of them is moving faster than motion Along a straight line/circular/ the other. Let us look at the motion of periodic vehicles moving on a road. Soldiers in a Activity 9.1 march past Look at Fig. 9.1. It shows the position Bullock cart of some vehicles moving on a road in moving on a the same direction at some instant of straight road time. Now look at Fig. 9.2. It shows the Hands of an position of the same vehicles after some athlete in a race time. From your observation of the two Pedal of a bicycle figures, answer the following questions: in motion Which vehicle is moving the fastest Motion of the Earth of all? Which one of them is moving the around the Sun slowest of all? The distance moved by objects in a Motion of a swing given interval of time can help us to Motion of a decide which one is faster or slower. For pendulum example, imagine that you have gone to It is common experience that the see off your friend at the bus stand. motion of some objects is slow while that Suppose you start pedalling your bicycle of some others is fast. at the same time as the bus begins to Reprint 2024-25  it is easy to decide whose speed is the highest. One who takes shortest time to cover the distance of 100 metres has the highest speed. 9.2 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. Fig. 9.1 Vehicles moving in the same direction on a road 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 faster. 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 kilometres per hour, it implies that it will cover a distance of Fig. 9.2 Position of vehicles shown in Fig. 9.1 after some time 50 kilometres in one hour. However, a car seldom moves with a constant speed move. The distance covered by you after for one hour. In fact, it starts moving 5 minutes would be much smaller than slowly and then picks up speed. So, that covered by the bus. Would you say when we say that the car has a speed of that the bus is moving faster than the 50 kilometres per hour, we usually bicycle? consider only the total distance covered We often say that the faster vehicle by it in one hour. We do not bother has a higher speed. In a 100-metre race whether the car has been moving with M OTION AND TIME 93 Reprint 2024-25 a constant speed or not during that they found that the sun rises everyday hour. The speed calculated here is in the morning. The time between one actually the average speed of the car. In sunrise and the next was called a day. this book we shall use the term speed Similarly, a month was measured from for average speed. So, for us the speed one new moon to the next. A year was is the total distance covered divided fixed as the time taken by the earth to by the total time taken. Thus, complete one revolution of the sun. Total distance covered Often we need to measure intervals Speed = Total time taken of time which are much shorter than a In everyday life we seldom find objects day. Clocks or watches are perhaps the moving with a constant speed over long most common time measuring devices. distances or for long durations of time. Have you ever wondered how clocks and If the speed of an object moving along watches measure time? a straight line keeps changing, its The working of clocks is rather motion is said to be non-uniform. On complex. But all of them make use of the other hand, an object moving along some periodic motion. One of the most a straight line with a constant speed well-known periodic motions is that of is said to be in uniform motion. In a simple pendulum. 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. In Class VI you learnt how to measure distances. But, how do we measure time? Let us find out. 9.3 MEASUREMENT OF TIME If you did not have a clock, how would (b) Table clock (a) Wall clock 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 (c) Digital clock definite intervals of time. For example, Fig. 9.3 Some common clocks 94 SCIENCE Reprint 2024-25  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. Activity 9.2 Set up a simple pendulum as shown in Fig. 9.4 (a) with a thread or string of length nearly one metre. Switch off any fans nearby. Let the bob of the pendulum come to rest at its A B mean position. Mark the mean O position of the bob on the floor below it or on the wall behind it. Fig. 9.4 (a) A simple Fig. 9.4 (b) Different To measure the time period of pendulum positions of the bob of an oscillating simple pendulum the pendulum we will need a stopwatch. However, if a A simple pendulum consists of a stopwatch is not available, a table small metallic ball or a piece of stone clock or a wristwatch can be used. suspended from a rigid stand by a To set the pendulum in motion, thread [Fig. 9.4 (a)]. The metallic ball is gently hold the bob and move it slightly called the bob of the pendulum. to one side. Make sure that the string Fig. 9.4 (a) shows the pendulum at attached to the bob is taut while you rest in its mean position. When the bob displace it. Now release the bob from its of the pendulum is released after taking displaced position. Remember that the it slightly to one side, it begins to move bob is not to be pushed when it is to and fro [Fig. 9.4 (b)]. The to and fro released. Note the time on the clock motion of a simple pendulum is an when the bob is at its mean position. example of a periodic or an oscillatory Instead of the mean position you may motion. note the time when the bob is at one of The pendulum is said to have its extreme positions. Measure the time completed one oscillation when its bob, the pendulum takes to complete 20 starting from its mean position O, moves oscillations. Record your observations M OTION AND TIME 95 Reprint 2024-25 in Table 9.2. The first observation shown cells. These clocks are called quartz is just a sample. Your observations could clocks. The time measured by quartz be different from this. Repeat this clocks is much more accurate than that activity a few times and record your by the clocks available earlier. observations. By dividing the time taken Units of time and speed for 20 oscillations by 20, get the time The basic unit of time is a second. Its taken for one oscillation, or the time symbol is s. Larger units of time are period of the pendulum. minutes (min) and hours (h). You Is the time period of your pendulum already know how these units are related nearly the same in all cases? to one another. Note that a slight change in the What would be the basic unit of initial displacement does not affect the speed? time period of your pendulum. Since the speed is distance/time, the Nowadays most clocks or watches basic unit of speed is m/s. Of course, it have an electric circuit with one or more could also be expressed in other units Table 9.2 Time period of a simple such as m/min or km/h. pendulum You must remember that the Length of the string = 100 cm symbols of all units are written in S.No. Time taken for 20 Time period singular. For example, we write 50 km oscillations (s) (s) and not 50 kms, or 8 cm and not 8 cms. 1. 42 2.1 Boojho is wondering how many seconds there are in a day and how 2. many hours in a year. Can you help 3. him? There is an interesting story about the discovery that the time period of a given pendulum 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. 96 SCIENCE Reprint 2024-25  Different units of time are used Many time measuring devices were depending on the need. For example, it used in different parts of the world before is convenient to express your age in the pendulum clocks became popular. years rather than in days or hours. Sundials, water clocks and sand clocks Similarly, it will not be wise to express are some examples of such devices. in years the time taken by you to cover Different designs of these devices were the distance between your home and developed in different parts of the world your school. (Fig. 9.5). How small or large is a time interval 9.4 MEASURING SPEED of one second? The time taken in saying Having learnt how to measure time and aloud “two thousand and one” is nearby distance, you can calculate the speed of one second. Verify it by counting aloud an object. Let us find the speed of a ball from “two thousand and one” to “two moving along the ground. thousand and ten”. The pulse of a normal healthy adult at rest beats about Activity 9.3 72 times in a minute that is about 12 Draw a straight line on the ground with times in 10 seconds. This rate may be chalk powder or lime and ask one of slightly higher for children. your friends to stand 1 to 2 m away from it. Let your friend gently roll a ball along the ground in a direction perpendicular Paheli wondered how time was to the line. Note the time at the moment measured when pendulum the ball crosses the line and also when clocks were not available. it comes to rest (Fig. 9.6). How much time does the ball take to come to rest? 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? M OTION AND TIME 97 Reprint 2024-25  (b) Sand clock (a) Sundial at Jantar Mantar, Delhi (c) Water clock Fig. 9.5 Some ancient time-measuring devices 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 9.3. 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 Fig. 9.6 Measuring the speed of a ball some living organisms are given in 98 SCIENCE Reprint 2024-25  Table 9.3 Distance moved and time taken by a moving ball Name of the group Distance moved by Time taken (s) Speed = Distance/ the ball (m) Time taken (m/s) Table 9.4, in km/h. You can calculate Time taken = Distance/Speed the speeds in m/s yourself. Rockets, launching satellites into earth’s orbit, often attain speeds up to Boojho wants to know 8 km/s. On the other hand, a tortoise whether there is any device can move only with a speed of about 8 that measures the speed. cm/s. Can you calculate how fast is the rocket compared with the tortoise? Once you know the speed of an You might have seen a meter fitted object, you can find the distance moved on top of a scooter or a motorcycle. by it in a given time. All you have to do Similarly, meters can be seen on the is to multiply the speed by time. Thus, dashboards of cars, buses and other Distance covered = Speed × Time vehicles. Fig. 9.7 shows the dashboard You can also find the time an object of a car. Note that one of the meters has would take to cover a distance while km/h written at one corner. This is moving with a given speed. called a speedometer. It records the Table 9.4 Fastest speed that some animals can attain S. No. Name of the object Speed in km/h Speed in m/s 320  10 0 0 1. Falcon 320 60  60 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 M OTION AND TIME 99 Reprint 2024-25  9.5 DISTANCE-TIME GRAPH You might have seen that newspapers, magazines, etc., present information in various forms of graphs to make it Table 9.5 Odometer reading at different times of the journey Time Odometer Distance from (AM) reading 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 Fig. 9.7 The dashboard of a car 10:00 AM 36620 km 80 km 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 9.5. Can you tell how far was the picnic Fig. 9.8 A bar graph showing runs scored by a spot from the school? Can you calculate team in each over the speed of the bus? Looking at the Table, Boojho asked Paheli whether she interesting. The type of graph shown in can tell how far they would have Fig. 9.8 is known as a bar graph. travelled till 9:45 AM. Paheli had no Another type of graphical representation answer to this question. They went to is a pie chart (Fig. 9.9). The graph shown their teacher. She told them that one in Fig. 9.10 is an example of a line graph. way to solve this problem is to plot a The distance-time graph is a line graph. distance-time graph. Let us find out how Let us learn to make such a graph. such a graph is plotted. 100 SCIENCE Reprint 2024-25 Oxygen Other gases Y X O X Nitrogen Fig. 9.9 A pie chart showing composition Y of air Y Fig. 9.11 x-axis and y-axis on a graph paper 80 70 Therefore, we shall use only the shaded 60 part of the graph shown in Fig. 9.11. 50 Weight (in kg) 40 Boojho and Paheli found out the 30 distance travelled by a car and the time 20 taken by it to cover that distance. Their 10 data is shown in Table 9.6. X 2 4 6 8 10 12 14 16 18 20 22 Table 9.6 The motion of a car Age (in year) S. No. Time (min.) Distance (km) Fig. 9.10 A line graph showing change in weight of a man with age 1. 0 0 2. 1 1 Take a sheet of graph paper. Draw two lines perpendicular to each other 3. 2 2 on it, as shown in Fig. 9.11. Mark the 4. 3 3 horizontal line as XOX'. It is known as 5. 4 4 the x-axis. Similarly mark the vertical line YOY'. It is called the y-axis. The point 6. 5 5 of intersection of XOX' and YOY' is known as the origin O. The two You can make the graph by following quantities between which the graph is the steps given below: drawn are shown along these two axes.  Draw two perpendicular lines to We show the positive values on the represent the two axes and mark x-axis along OX. Similarly, positive them as OX and OY as in Fig. 9.11. values on the y-axis are shown along  Decide the quantity to be shown OY. In this chapter we shall consider along the x-axis and that to be only the positive values of quantities. shown along the y-axis. In this case M OTION AND TIME 101 Reprint 2024-25  we show the time along the x-axis Y 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 O X distance on the respective axes according to the scale you have chosen. For the motion of the car Fig. 9.12 Making a graph mark the time 1 min, 2 min, … on Y the x-axis from the origin O. Similarly, mark the distance 1 km, 2 km … on the y-axis (Fig. 9.12).  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 9.6 shows that at time 0 min the distance moved is also O X zero. The point corresponding to this set of values on the graph will therefore be the origin itself. After 1 Fig. 9.13 Making a graph minute, the car has moved a distance of 1 km. To mark this set of values  Fig. 9.12 shows the set of points on look for the point that represents the graph corresponding to positions 1 minute on the x-axis. Draw a line of the car at various times. parallel to the y-axis at this point.  Join all the points on the graph as Then draw a line parallel to the shown in Fig. 9.13. It is a straight x-axis from the point corresponding line. This is the distance-time graph to distance 1 km on the y-axis. The for the motion of the car. point where these two lines  If the distance-time graph is a intersect represents this set of values straight line, it indicates that the on the graph (Fig. 9.12). Similarly, object is moving with a constant mark on the graph paper the speed. However, if the speed of the points corresponding to different object keeps changing, the graph can sets of values. be of any other shape. 102 SCIENCE Reprint 2024-25  Y X Fig. 9.14 Distance-time graph of the bus Generally, the choice of scales is not  the difference between the highest as simple as in the example given in and the lowest values of each Fig. 9.12 and 9.13. We may have to quantity. choose two different scales to represent  the intermediate values of each the desired quantities on the x-axis and quantity, so that with the scale the y-axis. Let us try to understand this chosen it is convenient to mark the process with an example. values on the graph, and Let us again consider the motion of  to utilise the maximum part of the the bus that took Paheli and her friends paper on which the graph is to be to the picnic. The distance covered and drawn. time taken by the bus are shown in Suppose that you are given a graph Table 9.5. The total distance covered by paper of size 25 cm × 25 cm. One of the the bus is 80 km. If we decide to choose a scale 1 km = 1 cm, we shall have to scales which meets the above conditions draw an axis of length 80 cm. This is and can accommodate the data of Table not possible on a sheet of paper. On the 9.5 could be other hand, a scale 10 km = 1 cm would Distance: 5 km = 1 cm, and require an axis of length only 8 cm. This Time: 6 min = 1 cm scale is quite convenient. However, the Can you now draw the distance-time graph may cover only a small part of graph for the motion of the bus? Is the the graph paper. Some of the points to graph drawn by you similar to that be kept in mind while choosing shown in Fig. 9.13? the most suitable scale for drawing a Distance-time graphs provide a graph are: variety of information about the motion M OTION AND TIME 103 Reprint 2024-25 when compared to the data presented point A. We then mark the point, T, on by a table. For example, Table 9.5 gives the graph at which this perpendicular information about the distance moved line intersects it (Fig. 9.14). Next, we by the bus only at some definite time draw a line through the point T parallel intervals. On the other hand, from the to the x-axis. This intersects the y-axis distance-time graph we can find the at the point B. The distance distance moved by the bus at any corresponding to the point B on the y- instant of time. Suppose we want to axis, OB, gives us the distance in km know how much distance the bus had covered by the bus at 8:15 AM. How travelled at 8:15 AM. We mark the point much is this distance in km? Can you corresponding to the time (8:15 AM) on now help Paheli to find the distance the x-axis (Fig. 9.14). Suppose this point moved by the bus at 9:45 AM? Can you is A. Next we draw a line perpendicular also find the speed of the bus from its to the x-axis (or parallel to the y-axis) at distance-time graph? Keywords Bar graph Oscillation Time period Graphs Simple pendulum Uniform motion Non-uniform motion Speed Unit of time What you have Learnt The distance moved by an object in a unit time is called its speed. Speed of objects help us to decide which one is moving faster than the other. The speed of an object is the distance travelled divided by the time taken to cover that distance. Its basic unit is metre per second (m/s). Periodic events are used for the measurement of time. Periodic motion of a pendulum has been used to make clocks and watches. Motion of objects can be presented in pictorial form by their distance-time graphs. The distance-time graph for the motion of an object moving with a constant speed is a straight line. 104 SCIENCE Reprint 2024-25  Exercises 1. Classify the following as motion along a straight line, circular or oscillatory motion: (i) Motion of your hands while running. (ii) Motion of a horse pulling a cart on a straight road. (iii) Motion of a child in a merry-go-round. (iv) Motion of a child on a see-saw. (v) Motion of the hammer of an electric bell. (vi) Motion of a train on a straight bridge. 2. Which of the following are not correct? (i) The basic unit of time is second. (ii) Every object moves with a constant speed. (iii) Distances between two cities are measured in kilometres. (iv) The time period of a given pendulum is constant. (v) The speed of a train is expressed in m/h. 3. A simple pendulum takes 32 s to complete 20 oscillations. What is the time period of the pendulum? 4. The distance between two stations is 240 km. A train takes 4 hours to cover this distance. Calculate the speed of the train. 5. The odometer of a car reads 57321.0 km when the clock shows the time 08:30 AM. What is the distance moved by the car, if at 08:50 AM, the odometer reading has changed to 57336.0 km? Calculate the speed of the car in km/min during this time. Express the speed in km/h also. 6. Salma takes 15 minutes from her house to reach her school on a bicycle. If the bicycle has a speed of 2 m/s, calculate the distance between her house and the school. 7. Show the shape of the distance-time graph for the motion in the following cases: (i) A car moving with a constant speed. (ii) A car parked on a side road. 8. Which of the following relations is correct? Distance (i) Speed = Distance × Time (ii) Speed = Time Time 1 (iii) Speed = (iv) Speed = Distance Distance  Time M OTION AND TIME 105 Reprint 2024-25  9. The basic unit of speed is: (i) km/min (ii) m/min (iii) km/h (iv) m/s 10. A car moves with a speed of 40 km/h for 15 minutes and then with a speed of 60 km/h for the next 15 minutes. The total distance covered by the car is: (i) 100 km (ii) 25 km (iii) 15 km (iv) 10 km 11. Suppose the two photographs, shown in Fig. 9.1 and Fig. 9.2, had been taken at an interval of 10 seconds. If a distance of 100 metres is shown by 1 cm in these photographs, calculate the speed of the fastest car. 12. Fig. 9.15 shows the distance-time graph for the motion of two vehicles A and B. Which one of them is moving faster? Fig. 9.15 Distance-time graph for the motion of two cars 13. Which of the following distance-time graphs shows a truck moving with speed which is not constant? (i) (ii) 106 SCIENCE Reprint 2024-25  (iii) (iv) Extend Learning — Activities and Projects 1. You can make your own sundial and use it to mark the time of the day at your place. First of all find the latitude of your city with the help of an atlas. Cut out a triangular piece of a cardboard such that its one angle is equal to the latitude of your place and the angle opposite to it is a right angle. Fix this piece, called gnomon, vertically along a diameter of a circular board a shown in Fig. 9.16. One way to fix the gnomon could be to make a groove along a diameter on the circular board. Next, select an open space, which receives sunlight for most of the day. Mark a line on the ground along the North-South direction. Place the sundial in the sun as shown in Fig. 9.16. Mark the position of the tip of the shadow of the gnomon on the circular board as early in the day as possible, say 8:00 AM. Mark the position of the tip of the shadow every hour throughout the day. Draw lines to connect each point marked by you with the centre of the base of the gnomon as shown in Fig. 9.16. Extend the lines on the circular board up to its periphery. You can use this sundial to read the time of the day at your place. Remember that the gnomon should always be placed in the North-South direction as shown in Fig. 9.16. Fig. 9.16 M OTION AND TIME 107 Reprint 2024-25  2. Collect information about time-measuring devices that were used in the ancient times in different parts of the world. Prepare a brief write up on each one of them. The write up may include the name of the device, the place of its origin, the period when it was used, the unit in which the time was measured by it and a drawing or a photograph of the device, if available. 3. Make a model of a sand clock which can measure a time interval of 2 minutes (Fig. 9.17). Fig. 9.17 4. You can perform an interesting activity when you visit a park to ride a swing. You will require a watch. Make the swing oscillate without anyone sitting on it. Find its time period in the same way as you did for the pendulum. Make sure that there are no jerks in the motion of the swing. Ask one of your friends to sit on the swing. Push it once and let it swing naturally. Again measure its time period. Repeat the activity with different persons sitting on the swing. Compare the time period of the swing measured in different cases. What conclusions do you draw from this activity? Did you know? The time-keeping services in India are provided by the National Physical Laboratory, New Delhi. The clock they use can measure time intervals with an accuracy of one-millionth of a second. The most accurate clock in the world has been developed by the National Institute of Standards and Technology in the U.S.A. This clock will lose or gain one second after running for 20 million years. 108 SCIENCE Reprint 2024-25