Distance travelled in the first \(20 \mathrm{~min}=\) speed \(\times\) time \(=60 \times \frac{20}{60}=20 \mathrm{~km}\)

Understanding the relationship between speed, time, and distance is fundamental in physics, enabling us to calculate how far an object travels over a given time at a constant speed. The formula connecting these three variables is quite straightforward: \( \text{Distance} = \text{Speed} \times \text{Time} \). This equation tells us that the distance travelled by an object is directly proportional to its speed and the time it has been moving.

For example, suppose a car is moving at a constant speed of 60 km/h. If we want to find out how far the car will travel in 20 minutes, we first need to translate the time into hours since our speed is in km/h. Upon converting 20 minutes into hours by dividing by 60, we get \( \frac{1}{3} \) hours. Next, we apply the formula: \( \text{Distance} = 60 \text{ km/h} \times \frac{1}{3} \text{ h} = 20 \text{ km} \). So the car will travel 20 kilometers in 20 minutes.

Physics problems often require the conversion of units to ensure that all measurements are in the same system and can therefore be directly compared or combined. In our example problem, the time was initially given in minutes, but since speed was given in kilometers per hour, converting time to hours was essential.

The general rule for unit conversion is understanding the basic relationships, such as 60 minutes equal 1 hour, or 1000 meters equal 1 kilometer. To convert minutes to hours, you divide the number of minutes by 60. If we have other units, like seconds to hours, we'd first convert seconds to minutes and then minutes to hours.

It's vital to be comfortable with these conversions to avoid errors in calculations. If time were mistakenly left in minutes, our final distance figure would be incorrect, potentially leading to significant misunderstandings in more complex physics scenarios.

Physics is a discipline built upon mathematical calculations that describe the natural world. From the basic speed-time-distance problem we've discussed to more complex phenomena, math is the language that provides clarity and predicts outcomes.

When performing these calculations, it's essential to follow a systematic approach: identify the knowns and unknowns, select the correct formula, perform any necessary unit conversions, and solve the problem step by step. Accuracy is important, which means double-checking that each value is in the right unit and each step follows logically from the last.

In our example, clear, step-by-step calculations allow us to confidently state that a vehicle traveling at 60 km/h for 20 minutes covers a distance of 20 km. This careful approach to calculation ensures a solid understanding and the ability to apply these skills to a wide range of physics problems.