Final Speed Calculation Of A Mobile Object After Acceleration

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Hey guys! Ever wondered how fast something is moving after it's been accelerating for a while? Today, we're diving into a classic physics problem that'll help us figure that out. We've got a mobile object that's been accelerating, and we need to calculate its final speed. Let's break it down step by step!

Understanding the Problem

In this physics problem, the core concept revolves around determining the final velocity of a mobile object undergoing constant acceleration. The key here is understanding how acceleration, time, and initial velocity interact to produce the final velocity. Acceleration, which is measured in units of distance per time squared (in this case, meters per second squared), tells us how much the velocity changes each second. Time, measured in seconds, gives us the duration over which the acceleration acts. And finally, the initial velocity is the speed at which the object was moving before the acceleration began. Now, before we jump into the nitty-gritty, let's get a clear picture of what we're dealing with. We know our mobile object has been accelerating at a rate of 0.7 meters per second squared. This means that for every second that passes, its speed increases by 0.7 meters per second. We also know that this acceleration has been happening for 36 seconds. That's a pretty significant amount of time, so we can expect the object's speed to have changed quite a bit. And, we're given that the final speed is 45.3 meters per second. So, our mission, should we choose to accept it (and we do!), is to figure out how to use these pieces of information to calculate the final speed of the object. To solve this, we'll be using one of the fundamental equations of motion in physics. This equation helps us connect acceleration, time, initial velocity, and final velocity. Understanding this relationship is crucial for solving not just this problem, but a whole range of physics scenarios involving motion. So, let's grab our thinking caps and dive into the exciting world of kinematics!

The Formula We Need

The equation we're going to use is one of the most fundamental formulas in kinematics, the branch of physics that deals with motion. This equation elegantly connects final velocity, initial velocity, acceleration, and time. It's like a magic formula that unlocks the secrets of moving objects! This formula is: v = u + at, where:

  • v is the final velocity (what we want to find).
  • u is the initial velocity (the starting speed).
  • a is the acceleration (the rate of change in speed).
  • t is the time (how long the acceleration lasts).

This equation is a cornerstone of physics because it encapsulates the relationship between these key variables in motion. It tells us that the final velocity of an object is equal to its initial velocity plus the product of its acceleration and the time over which it accelerates. In simpler terms, the faster you start, the more you accelerate, and the longer you accelerate, the faster you'll end up going. The beauty of this equation lies in its simplicity and versatility. It allows us to solve a wide range of problems involving constant acceleration, from calculating the speed of a car accelerating on a highway to determining the trajectory of a projectile in flight. But before we can plug in our numbers and get an answer, we need to make sure we understand what each variable represents in our specific problem. We've already identified that we're looking for the final velocity, v. We know the acceleration, a, is 0.7 meters per second squared, and the time, t, is 36 seconds. Now, we need to figure out the initial velocity, u. This is the speed the object had before it started accelerating at 0.7 meters per second squared. Once we have all these pieces, we can simply substitute them into the equation and solve for v. So, let's take a closer look at our problem statement and see if we can find the value of the initial velocity. This is a crucial step in solving the problem, and making sure we have the correct value for u will ensure that our final answer is accurate.

Plugging in the Values

Alright, let's get down to the nitty-gritty and plug in the values we have into our trusty formula: v = u + at. This is where the magic happens, guys! We're going to take the information we've gathered from the problem statement and use it to calculate the final speed of our mobile object. First, let's recap what we know. We're given that the acceleration, a, is 0.7 meters per second squared. This means that for every second the object moves, its speed increases by 0.7 meters per second. We also know that the time, t, is 36 seconds. This is the duration over which the object is accelerating. And finally, we know that the final speed, v, is 45.3 meters per second. Now, let's substitute these values into our equation. This gives us: 45.3 = u + (0.7 * 36). Notice how we've replaced the symbols with the actual numbers from our problem. This is a crucial step in solving any physics problem. It helps us translate the abstract concepts into concrete calculations. Now, we have an equation with one unknown, u, which represents the initial velocity. Our next step is to solve this equation for u. This will tell us the speed the object was moving at before it started accelerating. Once we know the initial velocity, we'll have all the pieces of the puzzle, and we can calculate the final speed. But before we jump into solving for u, let's take a moment to appreciate the power of this simple equation. It allows us to connect seemingly disparate quantities like acceleration, time, and velocity, and use them to predict the motion of objects. This is the essence of physics – using mathematical tools to understand and explain the world around us. So, let's roll up our sleeves and get ready to solve for u. The final answer is just around the corner!

Solving for the Unknown

Now comes the fun part – solving for the unknown! We've got our equation: 45.3 = u + (0.7 * 36). Our mission is to isolate u on one side of the equation so we can figure out its value. Think of it like a detective solving a mystery, guys! We need to carefully follow the clues and use our mathematical skills to crack the case. The first thing we need to do is simplify the right side of the equation. We have 0.7 multiplied by 36. If we do that calculation, we get 25.2. So, our equation now looks like this: 45. 3 = u + 25.2. We're getting closer! Now, we need to get u all by itself. To do that, we need to get rid of the 25.2 that's being added to it. The way we do that is by subtracting 25.2 from both sides of the equation. Remember, whatever we do to one side of the equation, we have to do to the other side to keep things balanced. So, if we subtract 25.2 from both sides, we get: 45.3 - 25.2 = u + 25.2 - 25.2. On the right side, the +25.2 and -25.2 cancel each other out, leaving us with just u. On the left side, we have 45.3 minus 25.2. If we do that subtraction, we get 20.1. So, our equation finally simplifies to: 20.1 = u. This is it! We've solved for u! We now know that the initial velocity of the mobile object was 20.1 meters per second. This means that before the object started accelerating, it was already moving at a pretty good clip. Now that we know the initial velocity, we have all the information we need to fully understand the motion of the object. We know where it started, how fast it was going, how quickly it accelerated, and how long it accelerated for. This is the power of physics – it allows us to make sense of the world around us by using mathematical tools and equations. So, let's celebrate our success in solving for u! We're one step closer to fully understanding this physics problem.

The Answer and Its Meaning

Alright, guys, drumroll please! We've done the calculations, we've solved the equation, and now it's time to reveal the answer. The question we set out to answer was: What is the final speed of the mobile object after accelerating at 0.7 meters per second squared for 36 seconds? And after all our hard work, we've found that the final speed, v, is 45.3 meters per second. Woohoo! But what does this number actually mean? Well, it tells us how fast the object was moving at the very end of the 36-second acceleration period. Remember, the object started with an initial velocity of 20.1 meters per second, and then it sped up at a rate of 0.7 meters per second every second for 36 seconds. So, by the end of that time, it was moving significantly faster – at 45.3 meters per second. To put that into perspective, 45.3 meters per second is roughly equivalent to 163 kilometers per hour, or about 101 miles per hour! That's pretty fast! This result highlights the power of acceleration. Even a relatively small acceleration, like 0.7 meters per second squared, can result in a significant increase in speed over time. This is why understanding acceleration is so crucial in physics and engineering. It helps us design everything from cars and airplanes to roller coasters and rockets. But the answer itself is just one part of the story. It's also important to understand how we arrived at the answer. We used a fundamental equation of motion, v = u + at, and we carefully plugged in the values we were given in the problem. We then used our algebraic skills to solve for the unknown variable, v. This process of problem-solving is just as important as the answer itself. It teaches us how to think logically, how to break down complex problems into smaller steps, and how to use mathematical tools to understand the world around us. So, congratulations, guys! We've not only solved a physics problem, but we've also honed our problem-solving skills. That's a win-win!

Real-World Applications

Okay, guys, so we've crunched the numbers and figured out the final speed of our mobile object. But you might be thinking,