Calculating Travel Time How Long To Reach A Gas Station At 90 Km/h

Hey guys! Ever wondered how to calculate travel time when you know the distance and speed? Let's dive into a classic physics problem that's super practical for everyday life. We're going to figure out how long it takes a driver to reach a gas station 500 meters away, traveling at 90 km/h. Buckle up, because we're about to break it down step by step!

Understanding the Problem: Speed, Distance, and Time

In this speed, distance, and time problem, we're given two key pieces of information the distance to the gas station (500 meters) and the speed the driver is traveling (90 km/h). Our mission is to find the time it takes to cover that distance. To do this, we'll use a fundamental formula in physics that relates these three quantities. This formula is like a magic key that unlocks the solution! Before we jump into the calculations, let's make sure we're all on the same page with units. Notice that the distance is given in meters (m), while the speed is in kilometers per hour (km/h). To keep things consistent, we'll need to convert the speed to meters per second (m/s). This conversion is crucial for accurate calculations. Think of it like speaking the same language – we need to have our units aligned to get the right answer. Now, why is this so important? Imagine trying to add apples and oranges – it doesn't quite work, right? Similarly, using mismatched units in our calculations will lead to a wrong result. So, let's make that conversion first. After converting, we'll have everything in a format that plays nicely together, and we can confidently apply our formula. This step of unit conversion is a common pitfall in physics problems, so it's always a good idea to double-check and make sure everything is in the same "language" before proceeding.

Converting km/h to m/s: A Crucial Step

Before we can apply the formula, we need to convert the km/h to m/s. The speed is given as 90 km/h, but our distance is in meters, so we need to get everything into the same units. Here's how we do it: First, remember that 1 kilometer (km) is equal to 1000 meters (m). Second, 1 hour (h) is equal to 3600 seconds (s). So, to convert from km/h to m/s, we multiply by 1000 (to convert kilometers to meters) and divide by 3600 (to convert hours to seconds). This might sound a bit complicated, but it's actually quite straightforward once you get the hang of it. Think of it as a recipe – you're just following the steps to get the desired result. Let's put it into action: 90 km/h * 1000 m/km / 3600 s/h = 25 m/s. See? Not so scary! We've successfully converted 90 km/h to 25 m/s. This means the driver is traveling at 25 meters every second. Now we have our speed in the correct units, and we're one step closer to solving the problem. This conversion is a key skill in physics, and you'll use it in many different scenarios. It's like learning a new word in a language – once you know it, you can use it in countless sentences. So, make sure you're comfortable with this process. Next, we'll plug this value into our formula and find out how long it takes to reach the gas station.

Applying the Formula: vm = δs/δt

Now for the fun part – using the formula! We're going to use the formula vm = δs/δt to find the time. Let's break down what each part means. vm stands for the average speed, which we know is 25 m/s (after our conversion, remember?). δs represents the distance traveled, which is 500 meters. And δt is the time it takes, which is what we're trying to find. The formula basically says that average speed is equal to the distance traveled divided by the time it took. It's a simple but powerful relationship. Think of it like this if you travel a longer distance at the same speed, it will take you more time. Conversely, if you travel at a higher speed over the same distance, it will take you less time. Now, let's rearrange the formula to solve for δt. We can do this by multiplying both sides of the equation by δt and then dividing both sides by vm. This gives us: δt = δs/vm. This is just a bit of algebraic manipulation, but it's a crucial step in solving for our unknown. We've now transformed the formula into a form that directly gives us the time. Next, we'll plug in our values for distance and speed and calculate the answer. It's like fitting the pieces of a puzzle together – we have all the information we need, and now we're ready to put it all together and see the solution.

Calculating the Time: Putting it All Together

Alright, time to put everything together and calculate the calculating the time. We have our rearranged formula: δt = δs/vm. We know δs (the distance) is 500 meters, and vm (the speed) is 25 m/s. So, we simply plug these values into the formula: δt = 500 m / 25 m/s. Now, it's just a matter of doing the division. 500 divided by 25 is 20. So, δt = 20 seconds. That's it! We've found our answer. It will take the driver 20 seconds to reach the gas station. This calculation is a perfect example of how physics can help us understand and predict things in the real world. We took a real-life scenario, applied a simple formula, and found a concrete answer. It's like having a superpower that lets you figure out how long things will take! This also highlights the importance of paying attention to units. Because we converted km/h to m/s, our answer came out in seconds, which makes sense in the context of the problem. If we had skipped that step, our answer would have been way off. So, always double-check your units! We've now successfully solved the problem. But let's take a moment to reflect on what we've done and how we can apply this knowledge to other situations.

Answer and Implications: 20 Seconds to the Gas Station

So, the final answer is 20 seconds! It will take the driver 20 seconds to reach the gas station 500 meters away while traveling at 90 km/h. This answer not only solves the specific problem but also gives us a sense of scale. Twenty seconds might seem like a short time, but at 25 m/s, you can cover a significant distance. This kind of calculation is useful in many real-world scenarios. For example, you might use it to estimate how long it will take to reach a destination while driving, or to figure out the timing for a train journey. It's also relevant in fields like sports, where athletes need to calculate speeds and distances to optimize their performance. Imagine a sprinter timing their run, or a cyclist planning their route – these calculations are essential. Moreover, this problem highlights the importance of understanding the relationship between speed, distance, and time. These concepts are fundamental in physics and are used in countless applications. From understanding the motion of planets to designing vehicles, the principles we've used here are everywhere. And it all boils down to that simple formula: vm = δs/δt. But remember, guys, physics isn't just about formulas. It's about understanding the world around us and using that understanding to solve problems. This example shows how a bit of physics knowledge can make you a more informed and efficient person.

Conclusion: Physics in Action

We've successfully solved a physics problem by converting units, applying a formula, and calculating the time it takes to reach a destination. It's a physics in action situation! This problem demonstrated how the concepts of speed, distance, and time are interconnected and how we can use a simple formula to relate them. By converting km/h to m/s, we ensured that our units were consistent, which is crucial for accurate calculations. We then applied the formula vm = δs/δt, rearranged it to solve for time, and plugged in our values to find the answer: 20 seconds. This exercise wasn't just about finding a number; it was about understanding the process and the underlying principles. We learned how to break down a problem into smaller steps, how to choose the right formula, and how to interpret the results. These are valuable skills that can be applied in many different areas of life. So, next time you're wondering how long it will take to get somewhere, remember this problem. You now have the tools to figure it out! And that's the beauty of physics – it gives you the power to understand and predict the world around you. Keep exploring, keep questioning, and keep applying these concepts. You never know when they might come in handy!

Answer: B) 20 segundos