Displacement & Average Velocity: Physics Problem Solved

Hey everyone! Let's dive into a classic physics problem involving motion in a straight line. We're going to break down how to calculate displacement and average velocity when an object moves at different speeds over different time intervals. This is a fundamental concept in physics, and understanding it will help you tackle more complex problems later on. So, let's get started!

The Problem: A Mobile's Journey

Imagine a mobile phone (or any object, really) traveling in a straight line. For the first 9 seconds, it zips along at an average speed of 1200 cm/s. Then, for the next 7 seconds, it slows down a bit to an average speed of 480 cm/s. The key thing here is that both speeds are in the same direction. This simplifies our calculations because we don't have to worry about changes in direction affecting the overall displacement. Our mission, should we choose to accept it, is to find two things:

• a) The total displacement of the mobile during the entire 16-second trip.
• b) The average velocity of the mobile over the whole journey.

Let's break down each part step by step.

a) Calculating Total Displacement: The Distance Traveled

In this section, we will focus on calculating the total displacement of the mobile during its 16-second journey. Displacement in physics refers to the overall change in position of an object, considering both the distance traveled and the direction. Since our mobile is moving in a straight line and the velocities are in the same direction, the displacement will simply be the total distance traveled. To find this, we'll break the journey into two segments and calculate the distance traveled in each segment. For the first segment, the mobile travels at 1200 cm/s for 9 seconds. To find the distance traveled, we use the fundamental formula: distance = speed × time. So, for this segment, the distance is 1200 cm/s × 9 s = 10800 cm. This means the mobile covered 10800 centimeters in the first 9 seconds. Now, let's consider the second segment of the journey. Here, the mobile slows down to an average speed of 480 cm/s and travels for 7 seconds. Again, we use the same formula: distance = speed × time. So, for this segment, the distance is 480 cm/s × 7 s = 3360 cm. In this part of the journey, the mobile traveled 3360 centimeters. To find the total displacement, we simply add the distances traveled in each segment. So, the total displacement is 10800 cm + 3360 cm = 14160 cm. Therefore, the total displacement of the mobile during the 16-second trip is 14160 cm. This means that, overall, the mobile's position changed by 14160 centimeters in the direction it was traveling. Remember, because the motion is in a straight line and the velocities are in the same direction, the displacement is equal to the total distance traveled. This makes the calculation straightforward: we just find the distance traveled in each part of the journey and add them up.

b) Finding the Average Velocity: Speed Over Time

Now, let's tackle the second part of our problem: finding the average velocity of the mobile over the entire 16-second journey. Average velocity isn't just about the speeds at different times; it's about the overall change in position (displacement) divided by the total time taken. This gives us a sense of the mobile's "average" speed and direction over the entire trip. We already know the total displacement from the previous calculation: it's 14160 cm. We also know the total time of the journey: 16 seconds. The formula for average velocity is simple: average velocity = total displacement / total time. Plugging in the values we have, we get average velocity = 14160 cm / 16 s. Performing the division, we find that the average velocity is 885 cm/s. So, the average velocity of the mobile over the 16-second journey is 885 centimeters per second. This means that, on average, the mobile was moving at a rate of 885 centimeters every second throughout its journey. It's important to note that this is an average value. The mobile was moving faster than this during the first part of the journey and slower during the second part, but overall, the average speed was 885 cm/s. Understanding average velocity helps us to get a general picture of the motion without focusing on the instantaneous speeds at every moment. It's a useful concept for describing motion over a period of time, especially when the speed is not constant.

Key Concepts and Takeaways

Let's recap the key concepts we've covered in this problem. We've looked at displacement, which is the overall change in position, and how to calculate it by considering the distance traveled in each segment of a journey. We also learned about average velocity, which is the total displacement divided by the total time. These concepts are fundamental to understanding motion in physics. When dealing with motion problems, always remember to consider the direction of motion. In this case, since the motion was in a straight line and the velocities were in the same direction, we could simply add the distances to find the total displacement. However, if the motion involved changes in direction, we would need to use vector addition to find the displacement. Understanding the difference between displacement and distance is crucial. Distance is the total length of the path traveled, while displacement is the overall change in position. They are the same only when the motion is in a straight line in one direction. Average velocity gives us a general sense of how fast an object is moving over a period of time. It's not the same as instantaneous velocity, which is the velocity at a specific moment in time. To solve motion problems effectively, break them down into smaller steps. Calculate the distances traveled in each segment of the journey, and then add them up to find the total displacement. Use the formula average velocity = total displacement / total time to find the average velocity. By mastering these fundamental concepts and techniques, you'll be well-equipped to tackle a wide range of motion problems in physics.

Practice Makes Perfect

To really solidify your understanding of these concepts, it's important to practice solving problems. Try changing the speeds and times in this problem and recalculating the displacement and average velocity. You could also try introducing a change in direction to make the problem more challenging. Remember, physics is all about understanding the relationships between different quantities. By practicing problem-solving, you'll develop a deeper understanding of these relationships and become more confident in your ability to apply them. Don't be afraid to make mistakes – they're a natural part of the learning process. When you encounter a problem you can't solve, take a step back, review the concepts, and try again. With practice and perseverance, you'll be well on your way to mastering motion in physics. So keep practicing, keep exploring, and most importantly, keep having fun with physics!