Calculating Distance Traveled A Car At 110 Km/h In 12 Minutes
In this article, we will delve into a classic physics problem involving the calculation of distance traveled by a car moving at a constant speed. This is a fundamental concept in kinematics, a branch of physics that deals with the motion of objects without considering the forces that cause the motion. Understanding how to calculate distance, speed, and time is crucial in many real-world applications, from planning road trips to understanding the motion of celestial bodies. We'll break down the problem step-by-step, ensuring clarity and a thorough understanding of the concepts involved. The problem we'll address is: A car travels at an average speed of 110 km/h. What distance does it cover in 12 minutes? This question requires us to convert units and apply the basic formula relating distance, speed, and time. Let's explore the concepts and calculations involved in solving this problem.
At the heart of this problem lies the relationship between speed, distance, and time. These three quantities are intrinsically linked, and understanding their relationship is key to solving problems in kinematics. Speed is defined as the rate at which an object covers distance. It is a scalar quantity, meaning it only has magnitude and no direction. The standard unit of speed in the International System of Units (SI) is meters per second (m/s), but it is also commonly expressed in kilometers per hour (km/h) or miles per hour (mph). Distance is the total length of the path traveled by an object. It is also a scalar quantity and is typically measured in meters (m), kilometers (km), miles (mi), or feet (ft). Time is the duration of an event or the interval between two events. The SI unit of time is seconds (s), but it is also frequently measured in minutes (min), hours (h), or days. The fundamental equation that connects these three quantities is:
Distance = Speed × Time
This equation tells us that the distance traveled by an object is equal to its speed multiplied by the time it travels. This equation can be rearranged to solve for speed or time if the other two quantities are known:
Speed = Distance / Time
Time = Distance / Speed
These formulas are the foundation for solving a wide range of motion problems. In our specific problem, we are given the speed of the car and the time it travels, and we are asked to find the distance it covers. However, there's a crucial step we need to consider before applying the formula: unit conversion. We are given the speed in kilometers per hour (km/h) and the time in minutes. To ensure consistency in our calculations, we need to convert either the speed to kilometers per minute or the time to hours. Let's delve into the unit conversion process.
In physics and mathematics, it is paramount to ensure that all quantities are expressed in consistent units before performing any calculations. This is where unit conversion becomes essential. In our problem, the car's speed is given in kilometers per hour (km/h), while the time is given in minutes. To use the formula Distance = Speed × Time effectively, we need to express both speed and time in compatible units. There are two primary approaches to handle this:
- Convert the time from minutes to hours.
- Convert the speed from kilometers per hour to kilometers per minute.
Let's explore each of these methods in detail:
Converting Time from Minutes to Hours
We know that there are 60 minutes in an hour. Therefore, to convert minutes to hours, we divide the number of minutes by 60. In our case, the time is given as 12 minutes. So, the conversion is:
Time (in hours) = 12 minutes / 60 minutes/hour = 0.2 hours
Now, we have the time in hours, which is consistent with the speed given in kilometers per hour. This conversion allows us to directly apply the formula Distance = Speed × Time using consistent units.
Converting Speed from Kilometers per Hour to Kilometers per Minute
Alternatively, we can convert the speed from kilometers per hour to kilometers per minute. To do this, we use the fact that there are 60 minutes in an hour. We divide the speed in km/h by 60 to get the speed in km/min. In our case, the speed is 110 km/h. So, the conversion is:
Speed (in km/min) = 110 km/h / 60 minutes/hour ≈ 1.833 km/min
Now, we have the speed in kilometers per minute, which is consistent with the time given in minutes. This conversion provides an alternative approach to solving the problem, ensuring we use compatible units.
By understanding and applying unit conversion, we ensure that our calculations are accurate and meaningful. This step is crucial in physics problems where quantities are often given in different units. Now that we have consistent units, we can proceed to apply the distance formula and solve for the distance traveled by the car. Let's move on to the next section where we'll perform the calculation and arrive at the final answer.
With the concepts of speed, distance, time, and unit conversion firmly in place, we can now proceed to calculate the distance traveled by the car. We have two options, thanks to our unit conversions: we can use the time in hours or the speed in kilometers per minute. Both approaches will yield the same result, providing a way to verify our calculations. Let's start by using the time in hours. We've already converted 12 minutes to 0.2 hours. The formula we'll use is:
Distance = Speed × Time
We know the speed is 110 km/h and the time is 0.2 hours. Plugging these values into the formula, we get:
Distance = 110 km/h × 0.2 hours = 22 km
So, the car travels 22 kilometers in 12 minutes when traveling at an average speed of 110 km/h. Now, let's verify this result by using the speed in kilometers per minute. We calculated the speed to be approximately 1.833 km/min. The time is given as 12 minutes. Using the same formula, we get:
Distance = 1.833 km/min × 12 minutes ≈ 21.996 km
This result is very close to 22 km, with the slight difference due to rounding in the speed conversion. This close agreement between the two calculations reinforces the accuracy of our approach and the importance of unit conversion. We have successfully calculated the distance traveled by the car using the fundamental relationship between speed, distance, and time. Now, let's formalize our answer and compare it with the provided options.
Having meticulously calculated the distance traveled by the car, we can now confidently state the solution. The car, traveling at an average speed of 110 km/h for 12 minutes, covers a distance of 22 kilometers. This result aligns perfectly with one of the provided options. Let's revisit the options:
A. 1320.00 km B. 550.00 km C. 22.00 km D. 9.17 km E. 0.36 km
Clearly, the correct answer is C. 22.00 km. The other options are significantly different from our calculated result, highlighting the importance of careful calculation and unit conversion. Options A and B are far too large, suggesting a misunderstanding of the time scale involved. Options D and E are too small, possibly arising from errors in unit conversion or misapplication of the formula. Our step-by-step approach, from understanding the concepts to unit conversion and calculation, has led us to the correct answer. This problem underscores the importance of a methodical approach in physics problem-solving, ensuring accuracy and avoiding common pitfalls.
In conclusion, we have successfully calculated the distance traveled by a car moving at an average speed of 110 km/h for 12 minutes. The problem highlighted the fundamental relationship between speed, distance, and time, as well as the critical importance of unit conversion in physics calculations. By converting the time from minutes to hours or the speed from kilometers per hour to kilometers per minute, we ensured consistency in our units and obtained an accurate result. The correct answer is 22 kilometers. This exercise demonstrates the practical application of kinematic principles and reinforces the importance of a step-by-step problem-solving approach. Understanding these concepts is not only crucial for academic success in physics but also for navigating real-world scenarios involving motion and travel. Whether it's planning a road trip or understanding the speed of a moving object, the principles we've discussed here are invaluable tools.
