(i) The unit of speed and velocity is \(\mathrm{m} \mathrm{s}^{-1}\). (ii) If a body is moving in a straight line path then its speed is equal to velocity \(50 \mathrm{~m} \mathrm{~s}^{-1}=50 \times \frac{18}{5} \mathrm{~km} \mathrm{~h}^{-1}=180 \mathrm{~km} \mathrm{~h}^{-1}\)

When we talk about how fast something is moving, we're referring to its speed. Speed is a measure of the distance an object travels over a certain period of time. The standard unit of speed in the International System of Units (SI) is meters per second, denoted as \(\mathrm{m} \mathrm{s}^{-1}\).However, depending on the context or region, different units may be used, such as kilometers per hour (\(\mathrm{km} \mathrm{h}^{-1}\)), miles per hour (mph), or knots (nautical miles per hour). These units are part of everyday use, for instance, when driving a car the speedometer usually displays the speed in miles per hour or kilometers per hour.Each of these units describes the same concept of speed but represents different scales of measurement. Converting between these units requires an understanding of the relationships between them, such as knowing how many meters are in a kilometer or how many seconds in an hour.

The conversion of speed units from meters per second to kilometers per hour is a common task in physics problems. To convert \(\mathrm{m} \mathrm{s}^{-1}\) to \(\mathrm{km} \mathrm{h}^{-1}\), one should consider that 1 kilometer is equal to 1000 meters, and 1 hour is equal to 3600 seconds.Thus, to convert the speed, you multiply the value in \(\mathrm{m} \mathrm{s}^{-1}\) by the factor \(\frac{3600}{1000}\), which simplifies to \(\frac{18}{5}\). This conversion factor directly relates the two units:\[ \text{Speed in } \mathrm{km} \mathrm{h}^{-1} = \text{Speed in } \mathrm{m} \mathrm{s}^{-1} \times \frac{18}{5} \]By applying this simple multiplication, one can easily switch between the two units, allowing for a better understanding of speed in different contexts, such as when comparing the speed of a car on the road (commonly km/h) to a runner's pace (often measured in m/s).

Velocity is a vector quantity that describes both the speed of an object and the direction in which it is moving. When an object is traveling along a straight path, its velocity and speed are essentially the same in terms of magnitude, but velocity will include directional information.For instance, if a car is moving eastward at a speed of 50 m/s, its velocity is 50 m/s east. In a straight line scenario with constant speed, the magnitude of the velocity remains the same—but remember, if the car changes direction or speed, the velocity will change accordingly even if the speed remains constant.In physics exercises and real-world applications, understanding the difference between speed and velocity is crucial for solving problems related to motion. It's important to note that while speed can never be negative, velocity can be, as it may indicate a change in direction rather than just a decrease in speed.

Physics numerical problems are exercises that require quantitative solutions, often involving calculations and the application of physics principles. These problems help students understand the practical applications of concepts they learn in class, such as speed, velocity, force, energy, and others.When approaching physics numerical problems, it’s essential to follow a systematic method:

• Clearly identify the given data and the physical quantities involved.
• Determine the relevant physics equations or principles that apply to the problem.
• Arrange the equation, isolate the unknown variable if necessary, and substitute the known values.
• Perform the calculation carefully, keeping in mind unit conversions and significant figures.
• Check that the final answer makes sense in the context of the problem: does it have the correct unit and physical significance?

Understanding the units involved, such as m/s or km/h for speed and the unit conversion process, is a vital skill for solving these problems accurately. Practice is key to becoming proficient in solving physics numerical problems, and students are encouraged to work through a variety of questions to develop their skills.