Calculating Car Acceleration: A Physics Problem

Hey guys! Let's dive into a classic physics problem: calculating the acceleration of a car. We'll break down the steps, use clear language, and make sure everything is easy to understand. This is a great example of how we use physics to describe the real world. So, grab your calculators and let's get started. Understanding acceleration is fundamental in physics, as it describes how an object's velocity changes over time. In this scenario, we have a car that speeds up, then slows down. We'll use this information to calculate its acceleration during both phases of its journey.

Phase 1: Accelerating the Car

Alright, let's start with the first part of the car's trip. The problem states that the car initially accelerates to a speed of 1200 km in 50 minutes. Before we do anything else, we gotta make sure our units are consistent. Physics loves its standard units, and in this case, we'll want to use meters (m) for distance, seconds (s) for time, and meters per second squared (m/s²) for acceleration. So, we need to convert our initial values.

First, let's convert the distance, which is 1200 km, to meters. We know that 1 kilometer (km) is equal to 1000 meters (m). Therefore, 1200 km is equal to 1200 * 1000 = 1,200,000 meters. Cool, one down.

Next up, we need to convert the time, which is 50 minutes, into seconds. We know that 1 minute is equal to 60 seconds. So, 50 minutes is equal to 50 * 60 = 3000 seconds. Awesome, we're making progress!

Now, we need to find the initial velocity and final velocity for this phase. Since the problem states the car starts, let's assume it starts from rest. Thus the initial velocity is 0 m/s. The final velocity, let's calculate that now.

We know that the car covers 1,200,000 meters in 3000 seconds. The formula to get the speed is simple: speed = distance / time. So, the car's velocity during this phase is 1,200,000 meters / 3000 seconds = 400 m/s. That's a speedy car!

Finally, the formula for calculating acceleration is:

acceleration = (final velocity - initial velocity) / time.

For phase 1, our initial velocity is 0 m/s, the final velocity is 400 m/s, and the time is 3000 seconds. Thus, the acceleration is:

acceleration = (400 m/s - 0 m/s) / 3000 s = 0.1333 m/s²

So, during the first part of its journey, the car has an acceleration of approximately 0.1333 m/s². That means its speed is increasing at a rate of 0.1333 meters per second, every second. This part of the calculation is a demonstration of uniform acceleration, where the velocity changes at a constant rate.

Phase 2: Decelerating the Car

Alright, now for the second part of the trip where the car decelerates. The problem tells us the car slows down to a speed of 600 km in 80 minutes. Again, let's convert those units!

First, convert 600 km to meters: 600 km * 1000 m/km = 600,000 meters.

Then, convert 80 minutes to seconds: 80 minutes * 60 seconds/minute = 4800 seconds.

Now, for this phase, our initial velocity is the final velocity from the first phase, which we calculated to be 400 m/s. We now need to calculate the final velocity for this phase, knowing that the car travels a distance of 600,000 meters in 4800 seconds. Again, we use the formula: velocity = distance / time.

So, the final velocity for this phase is 600,000 meters / 4800 seconds = 125 m/s. The car is definitely slowing down!

Now, we can calculate the acceleration using the same formula:

acceleration = (final velocity - initial velocity) / time

For phase 2, the initial velocity is 400 m/s, the final velocity is 125 m/s, and the time is 4800 seconds. Therefore:

acceleration = (125 m/s - 400 m/s) / 4800 s = -0.0573 m/s²

Notice that the acceleration is negative. This makes sense because the car is slowing down. The negative sign indicates deceleration, which means the car's velocity is decreasing. During this phase, the car's motion is non-uniform, as it is experiencing a negative acceleration, or deceleration.

Putting It All Together: Understanding the Car's Journey

So, in summary, we've calculated the car's acceleration in two phases: acceleration and deceleration. This problem highlights important concepts in physics, such as velocity, acceleration, and the importance of using consistent units. Remember that acceleration is the rate at which an object's velocity changes over time. A positive acceleration means the object is speeding up, while a negative acceleration (deceleration) means the object is slowing down. We've seen how to apply formulas and convert units to solve a real-world problem. By understanding these principles, we can better describe and predict the motion of objects around us. The two phases of the car's journey provide a great illustration of kinematics, the branch of physics that deals with the motion of objects without considering the forces that cause the motion. This problem offers a simple yet comprehensive example, showcasing how physics applies to everyday occurrences. We can further extend this analysis by considering the total distance traveled or the average acceleration over the entire journey.

Key Takeaways and Further Exploration

Here are some key takeaways from our acceleration problem:

• Units are crucial: Always use consistent units (meters, seconds) to avoid errors.
• Acceleration is a vector: It has both magnitude (how much) and direction (positive or negative).
• Deceleration: Negative acceleration indicates slowing down.
• Real-world applications: These concepts apply to many scenarios, such as rockets, and planes.

For further exploration, you can try variations of this problem. For example, you could calculate the average acceleration over the entire journey, considering both phases. You could also explore how different factors, such as the car's mass and the forces acting on it (friction, air resistance), affect its acceleration. Try changing the values, like the speed and time, to see how it changes the acceleration. Play around with different scenarios and have fun. The more you practice, the better you'll understand these physics concepts!

Keep in mind that this is a simplified model. In reality, the car's acceleration might not be perfectly constant. There might be slight variations due to factors like engine power, road conditions, and driver input. But for now, we've successfully tackled the problem and gained a clearer understanding of acceleration.

Hopefully, you found this explanation helpful, and now you have a better grasp of how to calculate acceleration. If you have any questions, feel free to ask. Keep experimenting, and keep learning! Physics is all around us, and with a little practice, you can master these concepts. This problem serves as a great introduction to the world of kinematics and provides a solid foundation for more complex physics problems. Stay curious, and keep exploring the amazing world of physics!