Satellite Distance: Calculating Travel In Seconds

Hey guys, let's dive into a classic physics problem! We're going to figure out how far a satellite traveled. This is a super common type of calculation, and understanding it is key to grasping some basic concepts in physics and math. So, the question is, how do we calculate the distance a satellite traveled?

We've got some key pieces of info: the satellite's speed and the time it was in motion. This problem uses the basic formula: distance = speed × time. It's that simple! But let's break down the process step by step to make sure we get it right, and talk about the nuances of units and significant figures. This will give you the complete picture of how to calculate the distance travelled by the satellite.

Understanding the Basics: Speed, Time, and Distance

Alright, before we get to the calculation, let's make sure we're all on the same page about the core concepts: speed, time, and distance. Imagine you're driving a car. The speed is how fast you're going—like 60 miles per hour. Time is how long you're driving—say, two hours. The distance is how far you traveled during that time—in this case, 120 miles. The relationship between these three is fundamental to understanding motion. This relationship works for anything that's moving, whether it's a car, a plane, or a satellite zooming around Earth. Speed is a measure of how quickly an object's position changes. Time is the duration over which the motion occurs. Distance is the total length of the path traveled. In this case, the satellite is traveling at a constant speed, and we're given the speed in meters per second (m/s) and the time in seconds (s). Because the units are compatible (both use seconds), we don't have to convert anything, making our calculation straightforward. So, we're going to directly use these values into our formula. Now, keep in mind, speed can change, or it can be constant. In our case, it's constant, which means it doesn't change over time. When we calculate distance, we're finding out how far the object moved during the time it was at that speed. Now, let's crunch some numbers!

Step-by-Step Calculation: Getting to the Answer

Let's get right into calculating the distance. So, the satellite's speed is 4283 meters per second, and it traveled for 2864 seconds. Here's how to calculate the distance: we'll use the formula: distance = speed × time. The calculation looks like this: Distance = 4283 m/s × 2864 s = 12,259,472 meters. So, the satellite traveled a total of 12,259,472 meters. Great, we've got our answer, but there's one more important step we need to consider: rounding to the correct number of significant figures. But why do we have to round? Well, in scientific calculations, the precision of our answer should match the precision of our input values. Significant figures tell us how precisely a measurement is known. Our speed and time values each have four significant figures. Therefore, our answer should also be expressed with four significant figures. Let's talk about the final step.

Rounding to Significant Figures: Precision Matters

Alright, rounding is crucial for scientific accuracy. When we perform calculations using measured values, our final answer's precision shouldn't exceed the precision of our original measurements. That's where significant figures come in. Significant figures are the digits in a number that contribute to its precision. The rules for significant figures tell us which digits are reliable and which are not. Let's look at the rules for rounding. In our case, the question asks us to round the answer to three significant figures. Let's apply this. We start with our unrounded answer: 12,259,472 meters. To round to three significant figures, we look at the first three digits: 1, 2, and 2. The next digit is 5, which is equal to or greater than 5, so we round up the last significant digit. So, 2 becomes 3, and the other digits after this point become zeros. So the number will be 12,300,000 meters. This is our final answer, but let's talk about it. So, the satellite traveled approximately 12,300,000 meters, which we can also write as 1.23 × 10^7 meters in scientific notation. Therefore, in the end, it is important to remember that significant figures show the precision of our results. Using the right number of significant figures makes sure that our answer makes sense in the context of our inputs. When we round our answer to three significant figures, we are maintaining the right level of accuracy based on the given information. So, rounding isn't just a formality. It's about respecting the precision of our initial measurements. The correct answer, when rounded to three significant figures, is 12,300,000 meters. Remember to always check the requirements to see the appropriate number of significant figures. Keep going!

Units and Conversions: A Quick Note

Okay, before we wrap up, a quick word about units. In this problem, we were given speed in meters per second and time in seconds, so our distance was automatically in meters. But what if the units were different? Let's say, for example, that the speed was given in kilometers per hour, and the time was given in seconds. That would mean we'd need to convert the units to be compatible before calculating the distance. This is an important step to make sure our answer is accurate. You would need to convert kilometers per hour to meters per second or seconds to hours. Correct unit conversions are important to make sure your final answer is correct. Units are the foundation of all calculations. Keeping track of the units throughout your calculations will help prevent errors and ensure that your final answer makes sense. So, always make sure you're using the same units for all the values in your equation. Without doing this, you'll end up with an incorrect answer. With our speed in m/s and time in s, the calculation was simple, but conversions can make things a little more complex. Always check the units, and convert if necessary!

Conclusion: You've Got This!

So there you have it, guys! We've calculated the distance the satellite traveled. We used the formula distance = speed × time, did the math, and rounded our answer to the correct significant figures. Remember, this basic principle applies to many real-world situations, so you've learned a valuable skill. Calculating distance is a fundamental concept in physics, and with practice, you'll get more comfortable with these types of problems. Keep practicing, and you'll get better!