Measurement of Distances

Introduction:

An object is said to be in motion if its position changes with time. An object is said to be at rest if its position does not change with time. When an object is in motion for some time, it covers some distance. This distance can be measured in various ways using various units.

Explanation:

Distance:

An object changes its position while in motion. This makes it cover some distance. The distance traveled by a body is the length of the path that it has traveled.

Suppose a person starts from the black location and reaches the red location by the road shown in the picture below. The person takes the road shown in yellow.

Here, the distance traveled by this person from the black location to the red location is the length of the path ABCDEF.

Thus, the distance covered = AB + BC + CD + DE + EF

Measuring Lengths:

In ancient times people used various units of measurement of length which were easily accessible to everyone such as the handspan, the cubit, the arm span, the pace, and the foot span.

However, everyone’s body parts are of slightly different sizes. Therefore, in 1790, the French created a standard unit of measurement called the metric system. Thus, for the sake of uniformity, scientists all over the world have accepted a set of standard units of measurement, which is known as the International System of Units or SI units.

Units of measurement of distances:

The SI unit of length is a meter. A meter rule is a device that is used to measure the length of various objects. It is of length 1 meter (m). There are smaller and larger units of measurement of length other than meters.

The units of measurement of length which are smaller than 1 meter (m) are centimeters (cm) and millimeters (mm).

1 m = 100 cm

1 cm = 10 mm

1 m = 1000 mm

A meter rule has the cm and mm marked on it.

It has 1 m divided into 100 equal parts, each part of length 1 cm, and each 1 cm part is divided into 10 equal parts, each of length 1 mm.

The units of measurement of length which are greater than 1 meter (m) are kilometer (km) and mile (mi).

1 km = 1000 m

1 mi = 1.609 km

1 mi = 1609 m

Large distances such as the distance between two cities are measured in the units of km or mi.

However, smaller distances such as the length of a table or the dimensions of a room are measured in the units of meter.

Questions and answers:

1. A person travels from city A to city F on the road shown. Find the distance traveled by the person.

Answer:

Total distance traveled

= AB + BC + CD + DE + EF

= 25 + 17 + 5 + 25 + 28

= 100 miles

Thus, the distance traveled by the person is 100 miles.

2. Which objects are in motion and at rest in the picture below? Fill in the blanks.

1. 7 km = —- m
2. 2 mi = —- m
3. 12 m = —– cm
4. 24 cm = —– mm
5. 2 m = —- mm

Answer:

1. 7 km = 7 x 1000 = 7000 m
2. 2 mi = 2 x 1609 = 3218 m
3. 12 m = 12 x 100 = 1200 cm
4. 24 cm = 24 x 10 = 240 mm
5. 2 m = 2 x 1000 = 2000 mm

3. The length of a sofa is measured using a meter rule. The length of the sofa turned out to be 2 and a half-length of the meter rule. What is its length?

Answer:

The length of a meter rule is 1 m.

The length of the sofa is 2 and a half of the meter rule.

Therefore, the length of the sofa

= 2.5 x 1 = 2.5 m