Motion and Time

Welcome dear students! Today we are going to learn about Motion and Time from Class 7 Science. In Class 6, 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? Let us look at some common examples. The motion of soldiers in a march past is along a straight line. The motion of a bullock cart moving on a straight road is along a straight line. The motion of the hands of an athlete in a race is along a straight line. The motion of the pedal of a bicycle in motion is circular. The motion of the Earth around the Sun is circular. The motion of a swing is periodic. The motion of a pendulum is periodic. [CHECKPOINT] It is common experience that the motion of some objects is slow while that of some others is 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. Let us look at the motion of vehicles moving on a road. Activity nine point one asks you to look at Figure nine point one. It shows the position of some vehicles moving on a road in the same direction at some instant of time. Now look at Figure nine point two. It shows the position of the same vehicles after some time. From your observation of the two figures, answer the following questions. Which vehicle is moving the fastest of all? The vehicle that has covered the maximum distance in the same time interval is moving the fastest. Which one of them is moving the slowest of all? The vehicle that has covered the minimum distance in the same time interval is moving the slowest. [CHECKPOINT] The distance moved by objects in a given interval of time can help us to decide which one is faster or slower. For example, imagine that you have gone to see off your friend at the bus stand. Suppose you start pedalling your bicycle at the same time as the bus begins to move. The distance covered by you after five minutes would be much smaller than that covered by the bus. Would you say that the bus is moving faster than the bicycle? Yes, we would. We often say that the faster vehicle has a higher speed. In a one hundred metre race it is easy to decide whose speed is the highest. One who takes shortest time to cover the distance of one hundred metres has the highest 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 faster. We call the distance covered by an object in a unit time as the speed of the object. [CHECKPOINT] When we say that a car is moving with a speed of fifty kilometres per hour, it implies that it will cover a distance of fifty kilometres 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 fifty kilometres 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, Speed equals Total distance covered divided by Total time taken. 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. In Class 6 you learnt how to measure distances. But, how do we measure time? Let us find out. [CHECKPOINT] 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. Figure nine point three shows some common clocks like a wall clock, a table clock, and a digital clock. A simple pendulum consists of a small metallic ball or a piece of stone suspended from a rigid stand by a thread as shown in Figure nine point four a. The metallic ball is called the bob of the pendulum. Figure nine point four 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 as shown in Figure nine point four 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. [CHECKPOINT] Let us perform Activity nine point two. Set up a simple pendulum as shown in Figure nine point four 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 mean position. Mark the mean position of the bob on the floor below it or on the wall behind it. To measure the time period of the pendulum we will need a stopwatch. However, if a stopwatch is not available, a table clock or a wristwatch can be used. To set the pendulum in motion, gently hold the bob and move it slightly to one side. Make sure that the string attached to the bob is taut while you displace it. Now release the bob from its displaced position. Remember that the bob is not to be pushed when it is released. Note the time on the clock when the bob is at its mean position. Instead of the mean position you may note the time when the bob is at one of its extreme positions. Measure the time the pendulum takes to complete twenty oscillations. Record your observations in Table nine point two. The first observation shown is just a sample. Your observations could be different from this. Repeat this activity a few times and record your observations. By dividing the time taken for twenty oscillations by twenty, get the time taken for one oscillation, or the time period of the pendulum. Is the time period of your pendulum nearly the same in all cases? Note that a slight change in the initial displacement does not affect the time period of your pendulum. Table nine point two shows a sample for a string length of one hundred centimetres. For the first observation, the time taken for twenty oscillations is forty two seconds, and the time period is two point one seconds. You will fill in the rest for your own experiment. [CHECKPOINT] Nowadays most clocks or watches have an electric circuit with one or more cells. These clocks are called quartz clocks. The time measured by quartz clocks is much more accurate than that by the clocks available earlier. The basic unit of time is a second. Its symbol is s. Larger units of time are minutes, written as min, and hours, written as 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 divided by time, the basic unit of speed is metres per second. Of course, it could also be expressed in other units such as metres per minute or kilometres per hour. You must remember that the symbols of all units are written in singular. For example, we write fifty kilometres and not fifty kilometres plural, or eight centimetres and not eight centimetres plural. Boojho is wondering how many seconds there are in a day and how many hours in a year. Can you help him? There are eighty six thousand four hundred seconds in a day and eight thousand seven hundred sixty hours in a year. 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 seventy two times in a minute that is about twelve times in ten seconds. This rate may be slightly higher for children. [CHECKPOINT] 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 as shown in Figure nine point five. Figure nine point five a shows a Sundial at Jantar Mantar, Delhi. Figure nine point five b shows a Sand clock. Figure nine point five c shows a Water clock. 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 Galilei, who lived from the year fifteen sixty four to sixteen forty two. 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. [CHECKPOINT] 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. Activity nine point three asks you to draw a straight line on the ground with chalk powder or lime and ask one of your friends to stand one to two metres away from it. Let your friend gently roll a ball along the ground in a direction perpendicular to the line. Note the time at the moment the ball crosses the line and also when it comes to rest as shown in Figure nine point six. 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 millennia. 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? [CHECKPOINT] 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 nine point three. In each case calculate the speed of the ball using the formula speed equals distance divided by time. 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 nine point four, in kilometres per hour. You can calculate the speeds in metres per second yourself. Table nine point four lists the fastest speed that some animals can attain. The Falcon has a speed of three hundred twenty kilometres per hour. The Cheetah has a speed of one hundred twelve kilometres per hour. The Blue fish has a speed of forty to forty six kilometres per hour. The Rabbit has a speed of fifty six kilometres per hour. The Squirrel has a speed of nineteen kilometres per hour. The Domestic mouse has a speed of eleven kilometres per hour. The Human has a speed of forty kilometres per hour. The Giant tortoise has a speed of zero point two seven kilometres per hour. The Snail has a speed of zero point zero five kilometres per hour. Rockets, launching satellites into earth orbit, often attain speeds up to eight kilometres per second. On the other hand, a tortoise can move only with a speed of about eight centimetres per second. Can you calculate how fast is the rocket compared with the tortoise? The rocket is one hundred thousand times faster than the tortoise. [CHECKPOINT] 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 equals Speed multiplied by Time. You can also find the time an object would take to cover a distance while moving with a given speed. Time taken equals Distance divided by 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. Figure nine point seven shows the dashboard of a car. Note that one of the meters has kilometres per hour written at one corner. This is called a speedometer. It records the speed directly in kilometres per hour. 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 thirty minutes till the end of the journey. Later on she recorded her readings in Table nine point five. At eight in the morning the odometer reading was thirty six thousand five hundred forty kilometres and distance from starting point was zero kilometres. At eight thirty in the morning the reading was thirty six thousand five hundred sixty kilometres and distance was twenty kilometres. At nine in the morning the reading was thirty six thousand five hundred eighty kilometres and distance was forty kilometres. At nine thirty in the morning the reading was thirty six thousand six hundred kilometres and distance was sixty kilometres. At ten in the morning the reading was thirty six thousand six hundred twenty kilometres and distance was eighty kilometres. Can you tell how far was the picnic spot from the school? It was eighty kilometres away. Can you calculate the speed of the bus? The speed is forty kilometres per hour. [CHECKPOINT] Looking at the Table, Boojho asked Paheli whether she can tell how far they would have travelled till nine forty five in the morning. 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. You might have seen that newspapers, magazines, and so on, present information in various forms of graphs to make it interesting. The type of graph shown in Figure nine point eight is known as a bar graph. It shows runs scored by a team in each over. Another type of graphical representation is a pie chart as shown in Figure nine point nine. It shows the composition of air with sections for Oxygen, Nitrogen, and Other gases. The graph shown in Figure nine point ten is an example of a line graph. It shows the change in weight of a man with age, plotting age in years on the horizontal axis and weight in kilograms on the vertical axis. The distance time graph is a line graph. Let us learn to make such a graph. Take a sheet of graph paper. Draw two lines perpendicular to each other on it, as shown in Figure nine point eleven. Mark the horizontal line as X O X prime. It is known as the x axis. Similarly mark the vertical line Y O Y prime. It is called the y axis. The point of intersection of X O X prime and Y O Y prime 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 O X. Similarly, positive values on the y axis are shown along O Y. In this chapter we shall consider only the positive values of quantities. Therefore, we shall use only the shaded part of the graph shown in Figure nine point eleven. [CHECKPOINT] 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 nine point six. The motion of a car is recorded as follows. At zero minutes, distance is zero kilometres. At one minute, distance is one kilometre. At two minutes, distance is two kilometres. At three minutes, distance is three kilometres. At four minutes, distance is four kilometres. At five minutes, distance is five kilometres. You can make the graph by following the steps given below. Draw two perpendicular lines to represent the two axes and mark them as O X and O Y as in Figure nine point eleven. 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: one minute equals one centimetre, and Distance: one kilometre equals one centimetre. 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 one minute, two minutes, and so on up to five minutes on the x axis from the origin O. Similarly, mark the distance one kilometre, two kilometres, up to five kilometres on the y axis as shown in Figure nine point twelve. Now you have to mark the points on the graph paper to represent each set of values for distance and time. Observation recorded at serial number one in Table nine point six shows that at time zero minutes the distance moved is also zero. The point corresponding to this set of values on the graph will therefore be the origin itself. After one minute, the car has moved a distance of one kilometre. To mark this set of values look for the point that represents one 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 one kilometre on the y axis. The point where these two lines intersect represents this set of values on the graph as shown in Figure nine point twelve. Similarly, mark on the graph paper the points corresponding to different sets of values. [CHECKPOINT] Figure nine point twelve 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 Figure nine point thirteen. 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 other shape. Generally, the choice of scales is not as simple as in the example given in Figure nine point twelve and nine point thirteen. 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 nine point five. The total distance covered by the bus is eighty kilometres. If we decide to choose a scale one kilometre equals one centimetre, we shall have to draw an axis of length eighty centimetres. This is not possible on a sheet of paper. On the other hand, a scale ten kilometres equals one centimetre would require an axis of length only eight centimetres. 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: 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. [CHECKPOINT] Suppose that you are given a graph paper of size twenty five centimetres by twenty five centimetres. One of the scales which meets the above conditions and can accommodate the data of Table nine point five could be Distance: five kilometres equals one centimetre, and Time: six minutes equals one centimetre. 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 Figure nine point thirteen? Distance time graphs provide a variety of information about the motion when compared to the data presented by a table. For example, Table nine point five 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 eight fifteen in the morning. We mark the point corresponding to the time eight fifteen in the morning on the x axis as shown in Figure nine point fourteen. Suppose this point is A. Next we draw a line perpendicular to the x axis at point A. We then mark the point, T, on the graph at which this perpendicular line intersects it. 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, O B, gives us the distance in kilometres covered by the bus at eight fifteen in the morning. How much is this distance in kilometres? It is ten kilometres. Can you now help Paheli to find the distance moved by the bus at nine forty five in the morning? Following the same method, the distance at nine forty five in the morning is seventy kilometres. Can you also find the speed of the bus from its distance time graph? Yes, it is forty kilometres per hour. [CHECKPOINT] Let us review the keywords from this chapter. Bar graph, Graphs, Non uniform motion, Oscillation, Simple pendulum, Speed, Time period, Uniform motion, 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. 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. Now let us solve the exercises from the textbook. Question one asks to classify the following as motion along a straight line, circular or oscillatory motion. One, motion of your hands while running. This is oscillatory motion. Two, motion of a horse pulling a cart on a straight road. This is motion along a straight line. Three, motion of a child in a merry go round. This is circular motion. Four, motion of a child on a see saw. This is oscillatory motion. Five, motion of the hammer of an electric bell. This is oscillatory motion. Six, motion of a train on a straight bridge. This is motion along a straight line. [CHECKPOINT] Question two asks which of the following are not correct. One, the basic unit of time is second. This is correct. Two, every object moves with a constant speed. This is not correct. Three, distances between two cities are measured in kilometres. This is correct. Four, the time period of a given pendulum is constant. This is correct. Five, the speed of a train is expressed in metres per hour. This is not correct. So the incorrect statements are two and five. Question three: A simple pendulum takes thirty two seconds to complete twenty oscillations. What is the time period of the pendulum? Time period equals total time divided by number of oscillations. That is thirty two divided by twenty, which equals one point six seconds. Question four: The distance between two stations is two hundred forty kilometres. A train takes four hours to cover this distance. Calculate the speed of the train. Speed equals distance divided by time. That is two hundred forty divided by four, which equals sixty kilometres per hour. Question five: The odometer of a car reads fifty seven thousand three hundred twenty one point zero kilometres when the clock shows the time eight thirty in the morning. What is the distance moved by the car, if at eight fifty in the morning, the odometer reading has changed to fifty seven thousand three hundred thirty six point zero kilometres? Calculate the speed of the car in kilometres per minute during this time. Express the speed in kilometres per hour also. Distance moved equals final reading minus initial reading. That is fifty seven thousand three hundred thirty six point zero minus fifty seven thousand three hundred twenty one point zero, which equals fifteen kilometres. Time taken is from eight thirty in the morning to eight fifty in the morning, which is twenty minutes. Speed in kilometres per minute equals fifteen divided by twenty, which equals zero point seven five kilometres per minute. To express in kilometres per hour, we multiply by sixty. So zero point seven five times sixty equals forty five kilometres per hour. [CHECKPOINT] Question six: Salma takes fifteen minutes from her house to reach her school on a bicycle. If the bicycle has a speed of two metres per second, calculate the distance between her house and the school. First, convert time to seconds. Fifteen minutes equals fifteen times sixty, which is nine hundred seconds. Distance equals speed multiplied by time. That is two times nine hundred, which equals one thousand eight hundred metres, or one point eight kilometres. Question seven: Show the shape of the distance time graph for the motion in the following cases. One, a car moving with a constant speed. The graph will be a straight line passing through the origin with a constant positive slope. Two, a car parked on a side road. The graph will be a horizontal straight line parallel to the time axis, showing distance does not change with time. Question eight: Which of the following relations is correct? One, speed equals distance times time. Two, speed equals distance divided by time. Three, speed equals time divided by distance. Four, speed equals one divided by distance times time. The correct relation is two, speed equals distance divided by time. Question nine: The basic unit of speed is: One, kilometres per minute. Two, metres per minute. Three, kilometres per hour. Four, metres per second. The correct answer is four, metres per second. [CHECKPOINT] Question ten: A car moves with a speed of forty kilometres per hour for fifteen minutes and then with a speed of sixty kilometres per hour for the next fifteen minutes. The total distance covered by the car is: First part: fifteen minutes is zero point two five hours. Distance equals forty times zero point two five, which is ten kilometres. Second part: fifteen minutes is zero point two five hours. Distance equals sixty times zero point two five, which is fifteen kilometres. Total distance equals ten plus fifteen, which is twenty five kilometres. The correct option is two, twenty five kilometres. Question eleven: Suppose the two photographs, shown in Figure nine point one and Figure nine point two, had been taken at an interval of ten seconds. If a distance of one hundred metres is shown by one centimetre in these photographs, calculate the speed of the fastest car. In the photographs, the fastest car moves the maximum distance. Let us assume from the visual that it moved two centimetres on the photograph. Two centimetres represents two hundred metres. Time is ten seconds. Speed equals two hundred divided by ten, which equals twenty metres per second. Note that the exact measurement depends on the printed figure, but using the given scale, you measure the distance in centimetres, multiply by one hundred to get metres, and divide by ten seconds. Question twelve: Figure nine point fifteen shows the distance time graph for the motion of two vehicles A and B. Which one of them is moving faster? Vehicle A has a steeper slope than vehicle B. A steeper slope on a distance time graph means a higher speed. Therefore, vehicle A is moving faster. [CHECKPOINT] Question thirteen: Which of the following distance time graphs shows a truck moving with speed which is not constant? Graph one is a straight line, showing constant speed. Graph two is a horizontal line, showing zero speed. Graph three is a curved line, showing changing speed. Graph four is a straight line, showing constant speed. Therefore, graph three shows a truck moving with speed which is not constant. Let us explore the extend learning activities. First, you can make your own sundial. Find the latitude of your city. Cut a triangular cardboard piece with one angle equal to your latitude and the opposite angle as a right angle. Fix this gnomon vertically along a diameter of a circular board. Place it in sunlight aligned North South. Mark the shadow tip every hour and connect to the centre. Second, collect information about ancient time measuring devices like water clocks and sand clocks. Third, make a sand clock model for two minutes. Fourth, measure the time period of a swing with and without a person sitting on it. You will observe that the time period remains nearly the same, just like a simple pendulum. 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 twenty million years. Thank you for listening! Keep revising and practicing. Goodbye! [CHAPTER_COMPLETE]