Question

A postman goes with a speed of \(36 \mathrm{~km} / \mathrm{h}\) what is the speed of postman in \(\mathrm{m} / \mathrm{s} ?\) (a) \(4.5 \mathrm{~m} / \mathrm{s}\) (b) \(6 \mathrm{~m} / \mathrm{s}\) (c) \(10 \mathrm{~m} / \mathrm{s}\) (d) can't be determined

Short answer

a) 9 m/s b) 9.2 m/s c) 10 m/s d) 10.8 m/s Answer: c) 10 m/s

Step-by-step solution

Write down the given speed

The postman's speed given is \(36 \mathrm{~km} / \mathrm{h}\).

Convert kilometers to meters

We need to convert 36 km to meters. To do this, we will use the conversion factor 1 km = 1000 m: \(36 \mathrm{~km} \times \dfrac{1000 \mathrm{~m}}{1 \mathrm{~km}} = 36000 \mathrm{~m}\)

Convert hours to seconds

Now, we need to convert 1 hour to seconds. We will use the conversion factor 1 hour = 3600 seconds: \(1 \mathrm{~h} \times \dfrac{3600 \mathrm{~s}}{1 \mathrm{~h}} = 3600 \mathrm{~s}\)

Calculate speed in meters per second

We have the distance in meters (36000 m) and the time in seconds (3600 s). Now, we can calculate the speed in meters per second: \(\mathrm{Speed ~in ~m/s} = \dfrac{36000 \mathrm{~m}}{3600 \mathrm{~s}} = 10 \mathrm{~m} / \mathrm{s}\)

Compare result with options

Our calculated speed is 10 m/s, which corresponds to option (c). Therefore, the speed of the postman in meters per second is: \(\boxed{10 \mathrm{~m} / \mathrm{s}}\) (Option c).

Key concepts

Speed Conversion

Understanding how to convert speed from one unit to another is a vital skill in physics and everyday life. In the case of the postman, we are presented with a common conversion: changing kilometers per hour (km/h) to meters per second (m/s). To make this conversion, you need to know two key conversion factors: one kilometer is equivalent to 1,000 meters, and one hour contains 3,600 seconds. By multiplying the given speed by the ratio of these two factors, you can seamlessly switch to the desired units. It's essential to keep track of the units throughout the process, ensuring that they cancel out appropriately to give you the final speed in the correct units of meters per second. This practical application of unit conversion is not only useful in academic settings but also in real-world scenarios, such as adjusting speedometer settings or interpreting speed limits when travelling abroad.

Relevance of Unit Conversion in Real Life

From cooking measurements to international travel, unit conversion skills allow us to navigate and understand different systems of measurement. For instance, understanding speed conversion is particularly important for athletes who travel for international competitions or engineers working with systems from various parts of the world.

SI Units

The International System of Units, or SI units, is the standard metric system used globally in science and industry. The SI unit for speed is meters per second (m/s). When the postman’s speed is given in kilometers per hour, it's not in the standard SI unit. For scientific consistency and to facilitate clear communication globally, converting to SI units becomes a necessity. Mastering these standard units allows for more accurate and universal understanding of scientific concepts. It's also important to note that in SI units, each physical quantity has a base unit, and speed is derived from the two base units: distance (meter) and time (second).

Advantages of Using SI Units

By adopting SI units, we ensure that the measurements we work with are widely understood and accepted. This uniformity is crucial for collaboration across international borders and in diverse scientific disciplines.

Quantitative Aptitude

Quantitative aptitude refers to the ability to handle numerical data, perform calculations, and solve problems involving numbers. In the context of the postman's speed problem, quantitative aptitude is demonstrated by manipulating the units and values to achieve the conversion. This skill is not limited to mathematics; it permeates daily decisions and professional tasks such as budgeting, time management, and technical analysis. Enhancing your quantitative aptitude involves practice and the application of logical strategies to break down complex numerical challenges into manageable steps. Simple acts like calculating the time it takes to travel a certain distance, or how to proportion ingredients in a recipe, can improve your quantitative skills.

Building Strong Quantitative Skills

Focus on becoming comfortable with numbers, relationships between units, and the algebra that often underpins problem-solving. Regular practice with a variety of problems can help build confidence and proficiency.

Math Problem Solving

Math problem solving is a critical thinking process in which a person uses mathematical concepts to find solutions to everyday situations and theoretical exercises, like our speed conversion example. In this case, we have followed logical steps to find the speed of the postman in meters per second from the initial information given in kilometers per hour. By breaking down the problem into a series of smaller, manageable steps, we make the solution more approachable and understandable. This structured approach to problem solving is key in math and can be applied to a wide range of disciplines and situations. By fostering these skills, students can learn to tackle complex problems systematically and efficiently.

Strategies for Effective Problem Solving

Some successful strategies include understanding the problem fully before jumping to solutions, identifying relevant information and discarding what's not needed, and methodically working through calculations while double-checking each step for accuracy. Encouraging these habits can pave the way for enhanced analytical skills in all aspects of life.