Measurement of Time and Motion

Long before anyone built a clock, people noticed that certain things in nature kept happening again and again at roughly the same intervals: the Sun rose and set once a day, the Moon changed shape over about a month, and the seasons cycled once a year. These repeating patterns became humanity's first calendars and first way of marking the passage of time.

People also needed to track much shorter stretches of time within a single day, and so they invented a range of clever devices. A sundial used the changing length and direction of a shadow cast by the Sun to show roughly what time of day it was. A water clock measured time by how steadily water dripped out of — or into — a marked container; one version used a small bowl with a tiny hole that floated on water and slowly filled up and sank at a fairly steady rate. An hourglass measured time through sand trickling from one glass bulb into another, and a candle clock used a candle marked at even intervals, so that a fixed amount of candle burning down meant a fixed amount of time had passed.

All of these early devices depended on finding some everyday process — a shadow moving, water dripping, sand falling, wax melting — that repeated or progressed at a reasonably steady, predictable rate. One of the most remarkable sundials ever built, the Samrat Yantra at the Jantar Mantar observatory in Jaipur, stands 27 metres tall and is accurate to about two seconds, with its shadow creeping across a carefully marked scale at roughly a millimetre every second. A major breakthrough in mechanical timekeeping came in the 1650s, when the Dutch scientist Christiaan Huygens built the first pendulum clock, inspired by earlier observations that a swinging pendulum takes a strikingly steady amount of time to complete each swing. Pendulum clocks were, for roughly the next two and a half centuries, the most accurate clocks in the world.

Today's clocks and watches have moved far beyond pendulums. Quartz watches use the extremely steady vibrations of a tiny quartz crystal, and atomic clocks use the vibrations of specific atoms — vibrations so remarkably steady that the best atomic clocks would lose only about one second over millions of years, compared to the pendulum clocks of the 1650s, which could drift by around ten seconds in a single day.

No matter how a clock is built, it is measured in the same standard units everywhere. The SI (international standard) unit of time is the second, written with the symbol s. Longer stretches of time are measured in minutes (min) and hours (h), related to the second as follows.

A simple pendulum is about as basic as a scientific instrument gets: a small, heavy object called a bob hangs from a thread tied to a fixed support. Left hanging straight down, it sits at its mean (resting) position. Pull the bob gently to one side and let it go, and it swings back and forth repeatedly — moving from its resting position out to one side, back through the resting position, out to the other side, and back again.

One full to-and-fro swing like this — from the mean position, out to one extreme, back through the middle, out to the other extreme, and back to the mean position — is called one oscillation. The time taken to complete exactly one oscillation is called the pendulum's time period.

Here is the genuinely useful part: for a pendulum of a fixed length, swinging at a particular location, the time period stays almost exactly the same every single time it is measured — whether the bob swings through a wide angle or a narrow one. This remarkable steadiness is exactly why pendulums were used to regulate clocks for centuries.

What actually changes a pendulum's time period? Its length does — a longer pendulum has a longer time period (it swings more slowly), while a shorter pendulum has a shorter time period (it swings faster). What does not change the time period, somewhat surprisingly, is the mass of the bob: a heavy bob and a light bob, swinging on threads of the exact same length, take the same time to complete one oscillation.

How would this time period actually be measured in practice? Timing just one single swing by hand is unreliable, since human reaction time while starting and stopping a stopwatch introduces a noticeable error. A much better method is to time several oscillations together and divide. For example, if a pendulum takes 20 seconds to complete 10 oscillations, its time period is 20 s ÷ 10 = 2 s — a far steadier reading than trying to time one single 2-second swing directly with human reflexes.

Watch a hundred-metre race: every runner starts at the same instant from the same line, but soon some runners pull ahead of others. The runner who has covered more distance in the same amount of time is running faster — in other words, that runner has a greater speed.

Speed is simply the distance covered by a moving object in a given amount of time. To calculate it for any journey, divide the total distance travelled by the total time taken to travel it.

Since distance is usually measured in metres and time in seconds, the SI unit of speed is metres per second, written m/s. For longer journeys, it is often more convenient to measure distance in kilometres and time in hours, giving speed in kilometres per hour, written km/h.

Suppose a cyclist covers 3 km in 10 minutes. To find her speed in m/s, first convert both quantities: 3 km is 3000 m, and 10 minutes is 600 s. Her speed is then 3000 m ÷ 600 s = 5 m/s.

Since the two units describe the very same quantity, it is possible to convert between them directly. One kilometre is 1000 m, and one hour is 3600 s, so 1 km/h works out to 1000 m ÷ 3600 s, which simplifies to 5/18 m/s. To convert a speed from km/h to m/s, multiply by 5/18; to go the other way, from m/s to km/h, multiply by 18/5. Checking the cyclist's speed this way: 5 m/s × 18/5 = 18 km/h — exactly matching what would be found by dividing 3 km directly by one-sixth of an hour (10 minutes).

The speed equation is useful in more ways than just calculating speed itself. Rearranged, it can show how far an object will travel in a given time if its speed is already known, or how long a journey will take if the distance and the speed are already known.

For example, a car travelling at a steady 60 km/h for 3 hours covers a distance of 60 km/h × 3 h = 180 km. Going the other way, if a bus needs to cover 150 km while travelling at a steady 50 km/h, it will take 150 km ÷ 50 km/h = 3 hours to complete the journey.

These same ideas are built into the instruments fitted in every car, bus, and scooter. A speedometer shows a vehicle's current speed, usually in km/h, while an odometer keeps a running total of the distance the vehicle has travelled, usually in kilometres. Together, they let a driver work out roughly how long any remaining stretch of a journey should take.

Picture a toy train gliding along a straight track at a perfectly steady speed, never speeding up or slowing down for as long as it is watched. In equal intervals of time — say, every single second — it covers exactly equal distances. This kind of motion, along a straight line at an unchanging speed, is called uniform linear motion.

Now picture something far more familiar: a bus travelling through city traffic, constantly speeding up between signals and slowing down to stop at the next one. In equal intervals of time, it covers unequal distances — sometimes a lot, sometimes very little, sometimes none at all while stopped. Motion like this, where the speed keeps changing along a straight path, is called non-uniform linear motion.

In practice, genuinely uniform motion over any real distance is quite rare and something of an idealised case. Even a car cruising on an empty highway briefly speeds up, eases off the accelerator, or adjusts slightly for a bend in the road. This is exactly why, for almost any real journey, average speed — the total distance covered divided by the total time taken for the whole journey — is used, rather than assuming the speed stayed perfectly constant throughout.

A good way to tell the two apart in data is to look at distances covered over several equal time intervals: if those distances stay the same interval after interval, the motion is uniform; if they vary from one interval to the next, it is non-uniform.