Educational Galaxy

Chapter 8: Measurement of Time and Motion — EG's own notes, in simple words

Book: Curiosity (CBSE, Class 7)  |  Chapter 8  |  Medium: English

Diagram (labels are printed on the image): A clock and a stopwatch for measuring time. The picture shows time-measuring instruments rather than a pendulum itself; it is a general picture, not a scene from the book.

A car moving along a road, covering distance over time. A general picture about motion, not a book scene.

What the chapter is about

Motion means change of position with time. An object is in motion if it changes its place with respect to its surroundings as time passes; otherwise it is at rest. To study motion we need to measure time and distance carefully. Time is measured in seconds, minutes and hours, and in the past people used devices like sundials, sand clocks and water clocks before the pendulum clock and modern watches.

A pendulum is a good example of repeated, or periodic, motion. A simple pendulum swings back and forth, and the time for one complete swing is called its time period. The time period depends mainly on the length of the pendulum, not on how heavy the bob is or how wide it swings, as long as the swing is small. Pendulum clocks use this steady beat to keep time.

Speed tells us how fast something moves. Speed equals distance divided by time, and its common unit is metres per second or kilometres per hour. If an object covers equal distances in equal times, its motion is uniform; if the distances differ, the motion is non-uniform. A distance-time graph shows this clearly: a straight sloping line means uniform motion, while a curved or changing slope means non-uniform motion.

8.1 Measurement of time

Long ago, people measured time by natural cycles — day and night, the phases of the Moon, the seasons — and announced the time of day with drums, conch shells or a gong. For smaller intervals within a day they used sundials, water clocks, hourglasses and candle clocks. In a sundial, the changing position of a shadow cast by sunlight tells the time. The world's largest stone sundial, the Samrat Yantra at Jantar Mantar in Jaipur, Rajasthan, is about 27 metres tall; its shadow moves about 1 millimetre per second and can measure intervals as short as 2 seconds. Like any sundial it measures local solar time, which needs a correction to give Indian Standard Time.

The pendulum changed timekeeping. Galileo noticed that a swinging pendulum takes the same time for each swing, whatever its swing size, as long as its length stays the same. A simple pendulum is a small heavy ball (the bob) hung by a thread from a rigid support. One full swing — from one extreme position to the other and back — is one oscillation, and the time for one oscillation is its time period. The time period depends on the length of the pendulum (a longer pendulum takes longer per swing) but not on the mass of the bob: bobs of different masses on the same length give the same time period. Pendulum clocks, first made by Huygens, used this steady beat. The SI unit of time is the second (s).

8.2 Slow or fast

To say who is faster, compare fairly: either the distance covered in the same time (more distance means faster) or the time taken for the same distance (less time means faster). Prerna, the chapter's sprinter, is judged by the time for 100 metres — the smallest time wins, even when two runners seem to finish together, which is why race timing must be so precise.

8.3 Speed

Speed is distance divided by time: speed = distance / time. Its SI unit is metre per second (m/s); speeds of vehicles are usually given in kilometre per hour (km/h). A vehicle's speedometer shows its speed in km/h and its odometer shows the distance it has travelled in kilometres. Because a real journey speeds up and slows down, the speed calculated from the whole distance and whole time is the average speed — and in this book the word speed is used to mean average speed.

Worked example from the chapter: Swati's school is 3.6 km from her house and she takes 15 minutes by bicycle. In hours, 15 minutes is 15/60 = 0.25 hour, so her speed is 3.6 / 0.25 = 14.4 km/h. Always convert minutes to hours (or kilometres to metres) before dividing, or the answer will be wrong even if the method is right.

8.4 Uniform and non-uniform linear motion

An object moving along a straight line at a constant speed is in uniform linear motion: it covers equal distances in equal intervals of time. If its speed along the straight line keeps changing, it is in non-uniform linear motion. A train may be non-uniform while speeding up, uniform on a clear stretch, and non-uniform again while slowing down — one journey can contain both kinds. In daily life, non-uniform motion is far more common: city traffic, with its stops and starts, is the classic example, while a car on an empty straight highway comes closest to uniform motion.

What you should learn

Learn to use speed equals distance divided by time, to recognise uniform and non-uniform motion, and to read a simple distance-time graph.

• Measure the time period of a pendulum and state what it does and does not depend on.
• Calculate speed from distance and time, converting units correctly, and read speedometers and odometers.
• Distinguish uniform from non-uniform linear motion with daily-life examples.

Chart / Table: Motion at a glance

Table: Motion at a glance

Steps: measuring a pendulum's time period

1. Hang a bob on a thread about 150 cm long from a rigid support and mark its rest position.
2. Pull the bob a little to one side, release it, and time 20 oscillations with a stopwatch.
3. Divide the total time by 20 to get one time period, and repeat to check the result.
4. Repeat with a longer thread, and then with a heavier bob on the same length, to see what changes the period.

Practice set — try it yourself

1. A car covers 60 km in 2 hours. What is its speed?
   Hint: Use speed = distance ÷ time.
2. What is the time period of a pendulum?
   Hint: Think about one complete swing.
3. How does a distance-time graph show uniform motion?
   Hint: Think about a straight sloping line.
4. Why is a pendulum clock steady?
   Hint: Think about repeated swings.
5. Is a bus stopping at stations in uniform motion? Why?
   Hint: Think about equal distances in equal times.

Questions with Answers

1. Define speed and calculate the speed of a cyclist who covers 30 km in 2 hours.
   Speed is distance covered per unit time. Speed = distance ÷ time = 30 km ÷ 2 h = 15 km/h.
2. What is a simple pendulum? On what does its time period mainly depend?
   A simple pendulum is a small heavy bob hung by a string from a fixed point, swinging back and forth. Its time period, the time for one complete swing, depends mainly on the length of the string, not on the mass of the bob.
3. What is the difference between uniform and non-uniform motion?
   In uniform motion an object covers equal distances in equal intervals of time. In non-uniform motion it covers unequal distances in equal intervals, as when a bus speeds up, slows down and stops.
4. How can you tell from a distance-time graph that motion is uniform?
   Uniform motion gives a straight line sloping upwards on a distance-time graph, because distance increases steadily with time. A flat line means the object is at rest.
5. Why are old clocks like sundials less reliable than pendulum clocks?
   Sundials depend on sunlight and cannot work at night or on cloudy days. A pendulum clock uses the steady, repeated swing of a pendulum, which keeps almost the same time period every time.

More questions with answers — extension

1. Distinguish uniform and non-uniform motion using a car on a straight highway with no traffic and a car in city traffic.
   The highway car, moving at a steady speed on a straight road, covers equal distances in equal times — uniform linear motion. The city car speeds up, slows down and stops, so its speed keeps changing — non-uniform linear motion, even though both cars move in straight lines at times.
2. A car covers 60 km in the first hour, 70 km in the second hour and 50 km in the third hour. Is the motion uniform? Find its average speed.
   Not uniform: the distance covered per hour changes (60, then 70, then 50 km), so the speed is not constant. Average speed = total distance / total time = (60 + 70 + 50) / 3 = 180 / 3 = 60 km/h.
3. An object's motion data: time 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 s and distance 0, 6, 10, 16, 21, 29, 35, 42, 45, 55, 60 m. Is its speed uniform or non-uniform? Find its average speed.
   Non-uniform: the distance gained every 10 seconds varies (6, 4, 6, 5, 8, 6, 7, 3, 10, 5 m), so the speed keeps changing. Average speed = 60 m / 100 s = 0.6 m/s.
4. A vehicle travels 2 km in a straight line in 200 s. In the first 500 m it moves at 10 m/s, in the next 500 m at 5 m/s. With what speed must it cover the remaining distance to finish in 200 s? What is its average speed for the whole journey?
   First 500 m take 500/10 = 50 s; next 500 m take 500/5 = 100 s. Time left = 200 − 50 − 100 = 50 s for the remaining 1000 m, so the required speed is 1000/50 = 20 m/s. Average speed for the whole journey = 2000 m / 200 s = 10 m/s.
5. Which type of motion is more common in daily life — uniform or non-uniform? Give three examples from your experience.
   Non-uniform motion is far more common. Examples: a bus stopping at bus stops, a cyclist slowing for a turn, and a person walking through a crowded market — in each, the speed keeps changing.
6. Does changing the bob's mass change a pendulum's time period? How would you test it?
   No. Keep the length fixed and repeat the time-period measurement with bobs of different masses; the time period stays the same. Changing the length, by contrast, does change it — a longer pendulum has a longer time period.
7. Why is a sundial's time not the same as Indian Standard Time?
   A sundial measures local solar time — the time told by the Sun's position at that place. Indian Standard Time is one common time for the whole country, so a place's solar time needs a correction (depending on its longitude) to match it.
8. A swing in a playground is like a pendulum. If children of different weights swing on the same swing, will their time periods be nearly the same? What if the swing's ropes are longer?
   Nearly the same: like the pendulum's bob, the child's weight (mass) hardly changes the time period. Longer ropes, however, give a longer time period — the swing takes longer for each swing, just as a longer pendulum does.
9. What might cause small differences in the time periods measured in repeated pendulum readings, and how can they be reduced?
   Small differences come from starting the stopwatch a fraction late or early, from counting a swing wrongly, or from the swing slowly shrinking. Timing many oscillations (for example 20) and dividing, then repeating the measurement, averages out these small errors.
10. Swati cycles 3.6 km in 15 minutes. A friend says her speed is 0.24 km/min and also 14.4 km/h. Are both right?
    Yes, both are the same speed in different units: 3.6 km / 15 min = 0.24 km/min, and 0.24 km/min × 60 min/h = 14.4 km/h. The chapter's answer is 14.4 km/h because vehicle speeds are usually quoted in km/h.

How to use this page: Read the summary, say the Key Terms in your own words, then try the practice set without looking. Use the Questions with Answers to check yourself afterwards. Ask your teacher or parent to check your answers.