Measurement of Time and Motion

1. Rest and Motion

When the position of an object changes with time with respect to a fixed point (a reference point), the object is said to be in motion. If its position does not change, it is said to be at rest.

Rest and motion are relative. A passenger sitting in a moving train is at rest with respect to the train and to fellow passengers, but is in motion with respect to a person standing on the platform. So whether a body is at rest or in motion depends on the observer's reference point.

1.1 Types of motion

• Rectilinear (linear) motion: motion along a straight line, e.g. a car on a straight road, a falling stone.
• Circular motion: motion along a circular path, e.g. the tip of a clock's hand, a stone whirled on a string.
• Periodic (oscillatory) motion: motion that repeats after a fixed time, e.g. the swing of a pendulum, a child on a swing.

2. The Need to Measure Time

People have always needed to measure time — to know when to sow crops, when to start a journey or when to gather. Early humans used events in nature that repeated regularly.

• The Sun: day and night, sunrise and sunset, and the changing length of shadows gave a sense of time.
• The Moon: the repeating phases of the Moon marked the month.
• The seasons: the repeating cycle of seasons marked the year.

Any event that repeats itself after a fixed interval can be used to measure time. This idea is the heart of every clock.

3. Early Time-Measuring Devices

Before modern clocks, several clever devices were used.

• Sundial: the position of the shadow of a fixed rod (gnomon) on a marked dial tells the time of day. It works only in sunlight.
• Water clock (clepsydra): water drips at a steady rate from one vessel to another; the level of water shows how much time has passed.
• Sand clock (hourglass): sand flows through a narrow neck from the upper to the lower bulb in a fixed time.
• Candle clock: a marked candle burns down at a steady rate, the markings showing the time.

A great step forward came when it was discovered that a swinging pendulum keeps very regular time, which led to the pendulum clock.

4. The Simple Pendulum

A simple pendulum is a small heavy ball (called the bob) hung by a light thread from a fixed support. When pulled to one side and released, it swings to and fro about its central (rest) position.

A very important fact: the time period of a given pendulum is constant — it does not depend on how far you pull the bob (for small swings) or on the mass of the bob. It depends mainly on the length of the thread: a longer pendulum has a larger time period (swings more slowly). Because the swing is so regular, the pendulum became the basis of accurate clocks.

5. Units of Time

The SI unit of time is the second (s). Larger units are built from it.

Very small intervals are measured in milliseconds (a thousandth of a second) and microseconds. Modern quartz and atomic clocks measure time extremely accurately, far better than any pendulum clock.

6. Speed — How Fast is an Object Moving?

Different objects move at different rates. A cheetah runs much faster than a person walking. The quantity that tells us how fast an object moves is called its speed.

6.1 Worked numericals

6.2 Converting km/h to m/s

7. Uniform and Non-Uniform Motion

Depending on whether the speed stays the same, motion is of two kinds.

• Uniform motion: the object covers equal distances in equal intervals of time; its speed is constant. Example: a car moving at a steady 60 km/h on a clear highway.
• Non-uniform motion: the object covers unequal distances in equal intervals of time; its speed keeps changing. Example: a bus in city traffic, speeding up and slowing down.

For non-uniform motion, we often talk about the average speed, which is the total distance travelled divided by the total time taken.

8. Distance–Time Graphs

The motion of an object can be shown clearly on a distance–time graph. Time is taken along the horizontal axis (x-axis) and distance along the vertical axis (y-axis).

• For an object at rest, the distance does not change, so the graph is a horizontal straight line.
• For an object in uniform motion, equal distances are covered in equal times, so the graph is a straight slanting (inclined) line.
• For non-uniform motion, the graph is a curved line.

Graphs help us compare two objects: the line with the greater slope (steeper line) belongs to the faster object. Graphs are widely used in science because they show at a glance how a quantity changes.