Why do we measure very small intervals of Time?
Time is not always measured only in seconds, minutes, or hours. In many situations, we need to measure very small fractions of a second.
For example, in a race, two athletes may finish almost together. The difference between their finishing times may be only a fraction of a second. Therefore, sports timing devices can measure time up to one-hundredth or even one-thousandth of a second.
A millisecond is one-thousandth of a second.
\(1\ millisecond=\frac{1}{1000}second\)
Very small time intervals are also important in medicine, music, computers, smartphones, and scientific experiments. For example, medical instruments can detect very small variations in heartbeats, while computers and smartphones process signals in extremely short intervals.
Measuring the smallest Time Interval of a Wall Clock:
A clock does not necessarily show every possible fraction of a second. The smallest time interval that a particular clock can measure depends on its design and display.
We can investigate this by observing the movement of the hands of a common wall clock.
For example, if the second hand moves from one second marking to the next, we can observe the smallest interval that the clock allows us to identify.
This activity helps us understand that different clocks and timing devices have different levels of precision.
A common wall clock is useful for measuring ordinary intervals of time, but very fast events require more precise instruments.
Slow or Fast – How do we know which object is Faster?
Imagine watching a \(100\ m\) race. All the runners start together, but after some time, they are at different positions on the track.
How can we decide who is running faster?
If two objects are moving for the same amount of time, the object that covers more distance is moving faster.
For example, suppose two children walk for \(10\ seconds\):
- Child \(A\) covers \(20\ m\).
- Child \(B\) covers \(30\ m\).
Child \(B\) has covered more distance in the same time. Therefore, Child \(B\) is moving faster.
However, simply looking at the position of an object is not always enough to decide its speed. An object may be farther ahead because it started earlier or travelled for a longer time.
Therefore, to compare whether an object is slow or fast, we need to consider the distance covered in a given amount of time.
What Is Speed?
We often use words such as fast and slow in everyday life. In science, we use the quantity called speed to describe how fast an object is moving.
Speed is the distance covered by an object in unit time.
To calculate the speed of an object, we need to know:
- The total distance covered
- The total time taken
The formula is:
\(Speed=\frac{Total\ distance\ covered}{Total\ time\ taken}\)
For example, if a cyclist covers \(100\ m\) in \(20\ s\):
\(Speed=\frac{100}{20}=5\ m/s\)
This means that, on average, the cyclist covers \(5\ metres\) in every second.
Units of Speed:
Since:
\(Speed=\frac{Distance}{Time}\)
the unit of speed depends on the units used for distance and time.
The SI unit of speed is \(meter\ per\ second (m/s)\)\( \)
because:
- SI unit of length is \(metre (m)\)
- SI unit of time is \(second (s)\)
Speed can also be expressed in \(kilometre\ per\ hour (km/h)\) when distance is measured in kilometres and time in hours.
Converting Units Before Calculating Speed
Sometimes the distance and time are given in units that do not match the required unit of speed.
For example, consider:
\(Distance = 3.6\ km\)
\(Time = 15\ minutes\)
If the answer is required in \(m/s\), we must first convert:
Distance:
\(1\ km\ = 1000\ m\)Therefore,
\(3.6\ km\ = 3600\ m\)Time:
\(1\ minute=60\ s\)
\(1\ minute=60\ s\)
Therefore,
\( \)\(15 min=900 s\)
Now:
\(Speed=\frac{3600}{900}=4\ m/s\)
Calculating and Comparing Train Speeds:
We can use a railway timetable to investigate the speeds of different trains.
Suppose we select a train and identify:
- The station from which it departs
- The next station where it stops
- The distance between the two stations
- The departure time
- The arrival time
First, calculate the time taken by the train.
Then use:
\(Speed=\frac{Distance}{Time}\)
The same procedure can be repeated for different types of trains, such as Passenger, Express, and Superfast trains.
Their calculated speeds can then be compared.