Measurement of Time and Motion

Why This Matters

Meet Prerna. She loves running. She is the fastest girl runner in her whole district. She won the 100 metre race at an inter-school meet. Now she dreams of running for India one day.

One evening, Prerna watched an old Olympic race on TV. Two runners crossed the finish line almost together. They looked exactly the same to her eyes. But the clock at the race could tell them apart. It measured time so finely that it knew who won — by a tiny fraction of a second.

That made Prerna think. Her sports teacher used a stopwatch. Her mother wears a watch. Her sister checks the time on her phone. There is a big clock near the school gate.

But what about people long ago? They had no watches. No phones. No clocks at all. So how did they know the time?

This chapter answers that. We will see how people measured time before clocks. We will meet the swinging pendulum that made clocks accurate. And we will learn how to measure motion — how to say exactly how fast something moves, and to prove who is faster. By the end, you will be able to do what that Olympic clock did: turn “fast” and “slow” into real numbers.

The Big Idea

To measure time, we look for something that repeats again and again, always taking the same gap — like the rising Sun, dripping water, or a swinging pendulum. We count those repeats, and that becomes our clock. The basic unit of time is the second. Once we can measure time, we can measure motion. The key idea is speed — how much distance an object covers in each unit of time. We find it with one simple rule: Speed = distance ÷ time. If an object covers the same distance every second, its motion is uniform. If the distance keeps changing, its motion is non-uniform.

Let’s Break It Down

Measuring time and its units

What does it even mean to “measure” time? We measure length with a scale. We measure weight with a balance. But time has no edges to measure with a ruler.

The trick people found long ago was this: find something in nature that repeats after the same gap every time. Then count the repeats.

Nature is full of such repeats. The Sun rises and sets, again and again. The Moon changes shape in a fixed cycle. The seasons return every year. People used these to make the very first calendars. A calendar is a way of counting days, months and seasons.

One full cycle of the Sun rising and setting gives us a day. But a day is a big gap. People wanted to measure smaller bits of time too — like the time within a single day. So they invented small clocks. We will meet those next.

Today we use fixed units for time. Let us pin them down.

How clocks evolved: sundial → water clock → pendulum clock

People did not get good clocks all at once. Better and better clocks were invented over hundreds of years. Each new one kept steadier time than the last. Figure 8.1 below lays them out as a timeline, oldest on the left.

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Let us look at each one.

The sundial. A sundial tells time using a shadow. A stick stands upright, and the Sun casts its shadow on a marked dial. As the Sun moves across the sky through the day, the shadow slowly moves too. You read the time from where the shadow falls. The world’s largest stone sundial, the Samrat Yantra at Jaipur’s Jantar Mantar, is 27 metres tall — its shadow moves about 1 millimetre every second. The catch: a sundial only works in daytime, and only when the Sun is out.

The water clock. A water clock measures time using flowing water. In one type, water drips slowly out of a marked vessel; you read the time from the falling water level. In another type used in ancient India (the Ghatika-yantra), a small bowl with a tiny hole floated on water. Water slowly seeped in until the bowl filled and sank — and each sinking marked a fixed gap of time (about 24 minutes). A water clock works at night too. But it was not very accurate, because as the water level dropped, the water dripped more slowly.

The pendulum clock. The big breakthrough came in the 1600s. A pendulum clock uses a swinging weight to keep time. It was so much steadier than anything before it that it changed timekeeping forever. We will study the pendulum closely next, because its steady swing is the heart of the story.

What do all three have in common? Each one is based on something that repeats — a shadow moving, water dripping, a bob swinging. Every clock, old or new, works this way. Even today’s most modern clocks follow the same idea, just with super-fast tiny vibrations (a quartz crystal in your watch, or special atoms in an atomic clock). Atomic clocks are so steady they lose only one second in millions of years.

The simple pendulum — its regular swing and time period

Here is a small experiment you can do at home. Tie a small heavy ball to a thread. Hang the thread from a fixed point, like a nail. This simple set-up is a pendulum.

The small heavy ball at the end is called the bob. The fixed point it hangs from is the rigid support (“rigid” means firm — it must not move).

Let the bob hang still. Where it rests, hanging straight down, is its mean position (mean just means “middle”). Now pull the bob gently to one side and let go. It swings to the other side, then back, then over again — back and forth, back and forth. This back-and-forth motion is called oscillation. Figure 8.2 below shows the whole swing.

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Two new words to lock in here:

• The two farthest points of the swing, one on each side, are the extreme positions (marked A and B in the figure).
• One full back-and-forth trip — say from A, through the middle O, across to B, and all the way back to A — is one oscillation.

Now the most important term. The time taken for one oscillation is called the time period of the pendulum. For example, if a pendulum takes 2 seconds to complete one full swing, its time period is 2 s.

Here is the magic part. If you measure the time period again and again, you get almost exactly the same value every time. A pendulum’s swing is wonderfully regular. This is what makes it a great clock: it ticks out equal gaps of time, over and over.

The time period of a simple pendulum of a given length stays the same at a place. This steady, repeating swing is what we use to measure time.

A tip for measuring it well: one single swing is too quick to time by hand. So time 10 oscillations instead, then divide by 10. For example, if 10 swings take 20 s, then one swing takes 20 ÷ 10 = 2 s. Dividing like this makes your answer more accurate.

One curious fact, first noticed by Galileo: the time period depends on the length of the thread, but not on how heavy the bob is. A longer thread gives a longer time period. But change the bob to a heavier one of the same length, and the time period stays the same.

But why does the pendulum keep such steady time? NCERT just tells you it does. Let us see why, because a curious mind should not have to take it on trust.

Think about what happens when you pull the bob out and release it. Gravity pulls it back towards the middle. Here is the clever balance, shown in Figure 8.3 below:

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So a wide swing has farther to travel, but it also moves faster. A narrow swing has less to travel, but it moves slower. The extra distance is paid for by extra speed — and the two cancel out. That is why every swing takes the same time, big or small. This neat balance is what makes the pendulum such a faithful timekeeper.

Describing motion

Now we move from time to motion. Motion just means movement — when an object changes its position. A running girl, a moving bus, a falling ball — all are in motion.

When something moves along a straight line, we call it linear motion (“linear” comes from line). A train going straight between two stations is in linear motion. We will stick to linear motion in this chapter.

Now think about Prerna’s 100 metre race. All the runners start together from the same line. But after a few seconds they are spread out. Some are ahead, some are behind. How do we decide who is running faster?

The answer is simple. In the same amount of time, the runner who has covered more distance is the faster one. Being ahead means going faster.

That works nicely when everyone runs the same distance, like 100 m. The one who finishes first is fastest. But what if two people run different distances — say one runs 100 m and another runs 400 m? Now we cannot just compare who is “ahead”. We need a fairer way to compare. That fair way is speed.

Speed = distance ÷ time

Speed tells us how fast something moves. Here is the exact meaning:

Speed = distance ÷ time

(Speed is the distance covered divided by the time taken to cover it.)

In words: speed is how much distance an object covers in each unit of time — for example, how many metres it covers in each second.

Why does dividing work? Imagine a runner covers 100 m in 20 s. To find out how much she covers in just one second, we share the 100 m equally over the 20 s: 100 ÷ 20 = 5 metres in each second. That “5 metres each second” is her speed. Dividing distance by time is exactly this sharing-per-second idea. Figure 8.4 below works through this number.

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What are the units of speed? Speed is distance ÷ time, so its unit is (unit of distance) ÷ (unit of time).

• If distance is in metres and time in seconds, speed is in metres per second, written m/s. This is the standard (SI) unit of speed.
• If distance is in kilometres and time in hours, speed is in kilometres per hour, written km/h. Car and train speeds are usually given this way.

So a speed of 5 m/s means “5 metres covered each second”. A speed of 60 km/h means “60 kilometres covered each hour”.

Let us put the formula to work on a real example, just like the one in your textbook.

The formula can be turned around. Sometimes you know the speed and want the distance or the time. Rearranging Speed = distance ÷ time gives two more handy forms:

distance = speed × time

time = distance ÷ speed

The helper triangle in Figure 8.4 is just a memory aid for these three forms — cover the one you want and read off the rest.

Uniform vs non-uniform motion

When something moves, it does not always keep the same speed. A bus speeds up, slows down, stops at a stop, then speeds up again. We sort motion into two types based on this.

Uniform motion means the speed does not change. The object covers equal distances in equal times. For example, if a car covers 20 m in the 1st second, 20 m in the 2nd second, 20 m in the 3rd second, and so on — same distance every second — it is in uniform motion.

Non-uniform motion means the speed keeps changing. The object covers unequal distances in equal times. For example, if a car covers 8 m in the 1st second, then 13 m, then 20 m — covering more each second — it is speeding up, so it is in non-uniform motion. Figure 8.5 below shows both side by side.

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In real life, almost everything moves in non-uniform motion. Buses, cars, people — they are always speeding up or slowing down a bit. Perfectly uniform motion is rare. That is why, when we calculate the speed of something over a whole journey, we are really finding its average speed — its overall speed for the trip, even though it sped up and slowed down along the way. In this chapter, whenever we say “speed”, we mean this average speed.

Let us put the two types side by side.

What to compare	Uniform motion	Non-uniform motion
Does the speed change?	No — speed stays the same	Yes — speed keeps changing
Distance in equal time gaps	Equal each time (e.g. 20 m, 20 m, 20 m)	Unequal (e.g. 8 m, 13 m, 20 m)
Dots on a track	Equally spaced	Unequally spaced
Everyday example	An ideal train cruising at a steady speed	A bus in city traffic, stopping and starting
Common in daily life?	Rare (an idealisation)	Very common

Common Mistakes

Some ideas in this chapter trip up many students. Let us clear them up before they cause trouble.

Quick Check

Try these short questions to test yourself. Each one reveals the answer with a short reason.

Practice Problems

Try each problem yourself first. Then tap to check the full step-by-step answer.

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Challenge

Summary

• To measure time, we count something that repeats with equal gaps — like the Sun’s daily cycle, dripping water, or a swinging pendulum.
• The SI unit of time is the second (s). The larger units are the minute and hour: 60 s = 1 min and 60 min = 1 h.
• Clocks improved over time: sundial → water clock → pendulum clock, and on to modern quartz and atomic clocks. Each one is built on a repeating process.
• A simple pendulum is a bob hanging by a thread. The time for one full swing (oscillation) is its time period. The time period stays steady, which makes the pendulum a good clock. It depends on the thread’s length, not the bob’s weight.
• Motion is a change in position. Motion along a straight line is linear motion.
• Speed = distance ÷ time — the distance covered in each unit of time. Its units are m/s or km/h. The formula can be rearranged: distance = speed × time, and time = distance ÷ speed.
• Uniform motion means equal distances in equal time gaps (speed unchanged). Non-uniform motion means unequal distances in equal time gaps (speed changing) — this is far more common in daily life.

What’s Next

You have learned to measure time and to describe motion with numbers. You can now find the speed of anything that moves — a runner, a bus, even a train between two stations.

Next, in Chapter 9 — Life Processes in Animals, we turn from the world of clocks and motion to the world of living things. You will discover the hidden machinery inside an animal’s body: how it takes in food, breathes, moves blood around, and gets rid of waste — all the processes that keep an animal alive. See you there.