Calculating Total Distance A Step By Step Guide

by Scholario Team 48 views

Hey guys! Let's break down this physics problem about a car's journey. We're going to calculate the total distance traveled by a car that moves at different speeds over different time intervals. It's like piecing together a road trip, segment by segment. We'll make it super clear and easy to follow, so you can totally nail similar problems in the future. So, buckle up and let's dive in!

Problem Statement: Unveiling the Car's Journey

Okay, so here's the scenario: A car embarks on a journey with varying speeds and durations. For the initial 30 minutes, it cruises along at 40 kilometers per hour (km/h). Then, it picks up the pace, traveling at 60 km/h for a full hour. Finally, for the last 15 minutes of its trip, it slows down to 20 km/h. The big question we need to answer is: What is the total distance the car covers throughout this entire journey? To get there, we'll also need to figure out the distance covered in each individual segment of the trip. It's like solving a mini-puzzle for each part of the journey and then adding them all up.

Breaking Down the Journey: Calculating Distance in Each Segment

To find the total distance, we need to calculate the distance traveled in each of the three segments. Remember the basic formula: Distance = Speed × Time. We'll apply this to each part of the journey, making sure our units (minutes and hours) align correctly. It's all about being precise and methodical.

Segment 1: The Initial 30-Minute Cruise

In this first leg, the car travels for 30 minutes at a speed of 40 km/h. Now, here's a crucial step: we need to convert those 30 minutes into hours because our speed is given in kilometers per hour. 30 minutes is exactly half an hour, or 0.5 hours. So, we can plug these values into our formula:

Distance₁ = Speed₁ × Time₁ = 40 km/h × 0.5 h

Calculating this, we get:

Distance₁ = 20 kilometers

So, the car covers 20 kilometers in the first 30 minutes of its journey. That's the first piece of our puzzle solved!

Segment 2: The One-Hour Stretch

Next up, the car travels at 60 km/h for a full hour. This part is a bit more straightforward since the time is already given in hours. Let's use our formula again:

Distance₂ = Speed₂ × Time₂ = 60 km/h × 1 h

This gives us:

Distance₂ = 60 kilometers

In this one-hour segment, the car covers a significant 60 kilometers. We're making good progress on figuring out the total distance!

Segment 3: The Final 15-Minute Slow Down

For the final part of the journey, the car slows down to 20 km/h and travels for 15 minutes. Again, we need to convert minutes to hours. 15 minutes is a quarter of an hour, or 0.25 hours. Plugging this into our formula:

Distance₃ = Speed₃ × Time₃ = 20 km/h × 0.25 h

Calculating this, we find:

Distance₃ = 5 kilometers

So, in the last 15 minutes, the car travels 5 kilometers. We've now calculated the distance for all three segments!

Putting It All Together: Calculating the Total Distance

We've calculated the distance for each segment of the journey: 20 kilometers, 60 kilometers, and 5 kilometers. Now, to find the total distance, we simply add these distances together:

Total Distance = Distance₁ + Distance₂ + Distance₃

Total Distance = 20 km + 60 km + 5 km

Total Distance = 85 kilometers

Therefore, the car travels a total of 85 kilometers during its entire journey. That's the final answer! We've successfully solved the problem by breaking it down into smaller, manageable parts.

Summarizing the Results: A Clear Overview

Let's recap what we've found:

  • Segment 1: 20 kilometers (30 minutes at 40 km/h)

  • Segment 2: 60 kilometers (1 hour at 60 km/h)

  • Segment 3: 5 kilometers (15 minutes at 20 km/h)

  • Total Distance: 85 kilometers

We've not only calculated the total distance but also broken down the journey into its individual segments, giving us a clear picture of the car's movements. It's like having a detailed travel log!

Why This Matters: Real-World Applications

Understanding how to calculate distance, speed, and time is super useful in many real-world situations. Think about planning a road trip, figuring out travel times, or even understanding the physics behind sports. These concepts are fundamental to understanding motion and are applied in various fields, from engineering to everyday life. So, mastering these calculations can really come in handy!

Key Takeaways: Mastering Distance Calculations

Here are the key things to remember from this problem:

  • The Formula: Distance = Speed × Time
  • Unit Conversion: Always make sure your units are consistent (e.g., convert minutes to hours if your speed is in km/h).
  • Breaking Down Problems: Complex problems can be solved by breaking them into smaller, simpler steps.
  • Real-World Relevance: These calculations have practical applications in everyday life.

By keeping these points in mind, you'll be well-equipped to tackle similar distance and speed problems. It's all about understanding the basics and applying them methodically.

Practice Makes Perfect: Try It Yourself!

Now that we've walked through this problem together, why not try one on your own? You can change the speeds, times, or even add more segments to the journey. The more you practice, the more comfortable you'll become with these calculations. It's like building a muscle for problem-solving!

So, grab a pen and paper, come up with your own scenario, and see if you can calculate the total distance. You've got this!

Conclusion: You've Got This!

We've successfully calculated the total distance traveled by the car by breaking the journey into segments and applying the formula Distance = Speed × Time. Remember, the key is to stay organized, pay attention to units, and take it one step at a time. You guys are now equipped to solve similar problems and understand the physics of motion a little better. Keep practicing, and you'll become a distance calculation pro in no time!

I hope this breakdown was helpful and clear. If you have any questions or want to try another example, just let me know. Happy calculating!