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Km-Hr To M-S In Fraction

By on Saturday, March 8, 2025
Km-Hr To M-S In Fraction

Understanding how to convert kilometers per hour (km/hr) to meters per second (m/s) is essential in physics, engineering, and daily life applications like speed calculations in vehicles or sports. While many people use the decimal conversion, it is also useful to express the result in fraction form, which provides greater accuracy and is commonly used in mathematical derivations.

This content will explain step-by-step how to convert km/hr to m/s in fraction form, provide examples, and explore why this conversion is important.

Basic Conversion Factor

To convert km/hr to m/s, we need to understand the basic relationship between kilometers, meters, hours, and seconds:

  1. 1 kilometer (km) = 1,000 meters (m)
  2. 1 hour (hr) = 60 minutes = 3,600 seconds (s)

Thus, the conversion factor from km/hr to m/s is:

1 , text{km/hr} = frac{1,000}{3,600} , text{m/s}

Simplifying this fraction:

frac{1,000}{3,600} = frac{5}{18}

Therefore, to convert any speed from km/hr to m/s, we multiply by 5/18.

Step-by-Step Conversion Process

Step 1: Identify the Speed in km/hr

Let’s say we need to convert 90 km/hr to m/s.

Step 2: Multiply by the Conversion Factor

Using the fraction 5/18, we multiply:

90 times frac{5}{18}

Step 3: Simplify the Fraction

Since 90 and 18 have a common factor (18), we simplify:

90 div 18 = 5
5 times 5 = 25

Thus,

90 , text{km/hr} = 25 , text{m/s}

Why Use Fraction Form Instead of Decimals?

  1. Higher Accuracy – Fractional values avoid rounding errors that occur in decimal approximations.
  2. Easier in Algebraic Manipulations – When working with formulas, fractions help in canceling units and simplifying expressions.
  3. Preferred in Scientific and Engineering Calculations – Many equations, such as those in physics and mechanics, use fractions for precise derivations.

Examples of Conversion Using Fractions

Example 1: Convert 72 km/hr to m/s

72 times frac{5}{18}

Simplifying:

72 div 18 = 4
4 times 5 = 20

Thus,

72 , text{km/hr} = 20 , text{m/s}

Example 2: Convert 108 km/hr to m/s

108 times frac{5}{18}

Simplifying:

108 div 18 = 6
6 times 5 = 30

Thus,

108 , text{km/hr} = 30 , text{m/s}

Example 3: Convert 36 km/hr to m/s

36 times frac{5}{18}

Simplifying:

36 div 18 = 2
2 times 5 = 10

Thus,

36 , text{km/hr} = 10 , text{m/s}

Reversing the Conversion: m/s to km/hr

To convert from m/s to km/hr, we use the reciprocal of the fraction 5/18, which is 18/5.

1 , text{m/s} = frac{18}{5} , text{km/hr}

For example, converting 25 m/s to km/hr:

25 times frac{18}{5}

Simplifying:

25 div 5 = 5
5 times 18 = 90

Thus,

25 , text{m/s} = 90 , text{km/hr}

Applications of km/hr to m/s Conversion

  1. Physics Problems – Speed, velocity, and acceleration calculations require consistent units.
  2. Automobile Speeds – Many vehicle speeds are given in km/hr but require conversion for time-distance problems.
  3. Sports and Athletics – Sprinting and running speeds are often measured in m/s.
  4. Engineering and Mechanics – Fluid flow, wind speed, and machinery operations use different units of speed.

Converting km/hr to m/s in fraction form is a crucial skill in physics and engineering. The conversion factor 5/18 simplifies the process and provides greater accuracy compared to decimal approximations. By understanding and practicing this method, you can handle speed-related calculations more efficiently in academic, professional, and real-world applications.

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