Calculating Displacement And Average Speed: A Physics Problem

Hey there, physics enthusiasts! Today, we're diving into a classic problem involving motion, displacement, and average speed. Let's break down the scenario step by step to understand how to solve it. We'll be using some basic kinematic equations, so buckle up and let's get started!

Understanding the Problem: The Mobile's Journey

Okay, so the problem sets the scene: a mobile, which we can think of as a car, a robot, or anything moving, is traveling in a straight line. This is a crucial detail because it simplifies our calculations. We're dealing with one-dimensional motion, meaning the object moves along a single axis (like the x-axis). The mobile goes through two phases of motion. In the first phase, it moves at a constant speed, and in the second phase, it also moves at a different constant speed.

Phase 1: High-Speed Travel

The mobile initially travels at an average speed of 1200 cm/s for 9 seconds. This information is essential because it tells us how fast the object is moving and for how long. The high speed is an important factor. During this time, the mobile covers a certain distance. To find this distance, we'll use a basic kinematic equation that relates speed, time, and distance. We will define the terms and the process to perform the calculation. You will understand how important it is to keep track of units and the significance of the result. Note that the distance traveled will be a scalar quantity, as the motion is in a straight line.

Phase 2: Slower Pace

After the initial burst of speed, the mobile transitions to a slower average speed of 480 cm/s for 7 seconds. Again, we have both the speed and the time for this phase of the journey. The second speed is slower. During this time, the mobile covers another distance, but at a reduced rate. We'll follow the same approach as in Phase 1 to calculate this distance. Keeping the units consistent is essential. It is worth noting how the change in speed impacts the displacement. You will see why the time is also important in this part.

The Questions

The problem asks two key questions:

1. What is the total displacement in the 16-second trip? Displacement is the change in position of the mobile. It's a vector quantity, so it has both magnitude and direction. In this case, since the motion is along a straight line, the direction is simply the direction of the motion. The total displacement is the sum of the displacements in both phases.
2. What is the average speed of the mobile? Average speed is the total distance traveled divided by the total time taken. The average speed gives an idea of how fast the mobile was moving overall during the entire trip. We will learn how to calculate it from the total distance and the total time.

Now, let's get into the calculations. We will take it step by step so you don't miss anything. We will calculate the displacement, so pay attention. Let's solve this problem! This is the most important part of the problem. Are you ready? Let's go!

Solving for Displacement: Breaking Down the Journey

Alright, let's get down to the nitty-gritty and calculate the displacement for each phase of the mobile's trip. Remember, the displacement is a vector quantity, meaning it has both magnitude (how far) and direction. Because the motion is along a straight line, the direction is straightforward: it's the direction the mobile is moving. We will now find the displacement in phase 1 and then in phase 2.

Displacement in Phase 1: High-Speed Run

In the first 9 seconds, the mobile moves at a speed of 1200 cm/s. The fundamental formula we'll use here is:

displacement = speed × time

So, for Phase 1:

• Speed = 1200 cm/s
• Time = 9 s

Therefore, displacement in Phase 1 = 1200 cm/s × 9 s = 10800 cm. In this case, since the speed is positive, the displacement is also positive.

Displacement in Phase 2: Slower Pace

Now, let's calculate the displacement during the second phase. The mobile travels at 480 cm/s for 7 seconds. Using the same formula:

• Speed = 480 cm/s
• Time = 7 s

Therefore, displacement in Phase 2 = 480 cm/s × 7 s = 3360 cm. In this part, the speed is also positive; therefore, the displacement is also positive. It is important to remember that it is also in the same direction, so the mobile continues moving in the same direction.

Total Displacement: Putting it Together

The total displacement is simply the sum of the displacements in both phases. We've got the displacement in Phase 1 and the displacement in Phase 2. To get the total displacement, we just need to add the two values we calculated:

Total Displacement = Displacement in Phase 1 + Displacement in Phase 2 Total Displacement = 10800 cm + 3360 cm = 14160 cm

So, the total displacement of the mobile in the 16-second trip is 14160 cm. This is the first part of our problem solved! Now we move to the next part. Congratulations!

Calculating Average Speed: The Overall Picture

We've found the total displacement. Now, let's find the average speed of the mobile for the entire 16-second trip. Remember, average speed is the total distance traveled divided by the total time taken. Since we have the displacement, we can calculate the average speed.

Total Distance Traveled

First, let's think about the total distance traveled. In this case, since the mobile is moving in a straight line and we are considering the magnitude of the movement, the total distance traveled is equal to the total displacement (14160 cm).

Total Time Taken

The total time is given in the problem: 16 seconds.

Calculating Average Speed

The formula for average speed is:

average speed = total distance / total time

Plugging in our values:

average speed = 14160 cm / 16 s = 885 cm/s

So, the average speed of the mobile during the 16-second trip is 885 cm/s. This means that, on average, the mobile was moving at 885 cm every second during the entire trip. Congratulations, you finished the problem!

Summary and Key Takeaways

Let's recap what we've learned and the key takeaways from this problem:

• Understanding the problem: We started by carefully reading and understanding the problem, identifying the given information (speeds, times) and the questions (displacement, average speed).
• Breaking down the motion: We divided the motion into two phases to make the calculations easier. This technique is often useful when dealing with motion with changing speeds or accelerations.
• Using kinematic equations: We used the basic kinematic equation: displacement = speed × time to calculate the displacement for each phase.
• Calculating total displacement: We added the displacements of each phase to find the total displacement.
• Calculating average speed: We used the formula average speed = total distance / total time to calculate the average speed.
• Units: It's very important to keep track of the units! In this case, we used centimeters for distance and seconds for time, which gave us a final answer in cm/s.

This problem illustrates a fundamental concept in physics: understanding motion and how to calculate displacement and speed. By breaking down the problem into smaller parts and using the right equations, we were able to solve it step by step. I hope this was useful. Keep practicing, and you'll become a pro at these problems! If you have any other questions or problems that you would like me to help you solve, please feel free to ask me!

Keep learning and have fun! You are amazing!