Calculating Velocity A 5kg Body Under Constant Force

Hey guys! Ever wondered how to calculate the velocity of an object when it's subjected to a constant force? Let's dive into a classic physics problem that illustrates this concept perfectly. We'll break it down step-by-step, making sure it's super clear and easy to follow. So, grab your thinking caps, and let's get started!

Understanding the Problem: Force, Mass, and Motion

In this fascinating physics scenario, we have a 5kg body that starts off completely still – that's what we mean by 'initially at rest.' Now, imagine a constant force of 30N acting on this body. The big question we're tackling today is: what will the body's velocity be after 5 seconds? This is a classic application of Newton's laws of motion, and understanding it helps us grasp how forces influence the movement of objects around us. This problem beautifully encapsulates the relationship between force, mass, and acceleration, ultimately leading to a change in velocity. It’s not just about plugging numbers into a formula; it’s about understanding the fundamental principles that govern motion. The beauty of physics lies in its ability to predict and explain these real-world scenarios with mathematical precision.

To fully appreciate the solution, we need to remember that force is what causes a change in motion. A larger force will generally cause a greater change in motion, but the mass of the object also plays a crucial role. A heavier object will resist changes in its motion more than a lighter object. This resistance is what we call inertia. The interplay between force, mass, and inertia is perfectly described by Newton's Second Law of Motion, which we'll use to solve this problem. Thinking about these concepts helps to build a strong foundation for understanding more complex physics problems in the future. For instance, this understanding is crucial when analyzing projectile motion, orbital mechanics, and even the behavior of objects in collisions. So, let's put on our physics hats and solve this exciting problem together!

Applying Newton's Second Law: The Key to Unlocking Velocity

Now, to find the solution, we need to turn to one of the cornerstones of classical mechanics: Newton's Second Law of Motion. This law, often expressed as the equation F = ma, is our key to unlocking the relationship between force (F), mass (m), and acceleration (a). In simpler terms, it tells us that the force acting on an object is equal to the mass of that object multiplied by its acceleration. This law is the bridge that connects the force applied to the body with the change in its motion. It’s a powerful tool that allows us to quantify how forces influence the movement of objects. Understanding this law is absolutely fundamental to understanding mechanics, and it’s the foundation upon which much of classical physics is built.

In our specific problem, we know the force (30N) and the mass (5kg). What we don't know, and what we need to find, is the acceleration (a). Once we determine the acceleration, we can then use kinematic equations to figure out the final velocity. So, let's rearrange the formula F = ma to solve for a: a = F / m. This simple algebraic manipulation is crucial for isolating the variable we want to find. Plugging in the values, we get a = 30N / 5kg = 6 m/s². This calculation tells us that the body is accelerating at a rate of 6 meters per second squared. That means its velocity is increasing by 6 meters per second every second. This is a significant piece of the puzzle, and it sets us up perfectly for the next step, where we'll use this acceleration to determine the final velocity after 5 seconds. So, we're well on our way to solving this problem, guys!

Calculating Acceleration: Putting Numbers to the Law

Alright, so we've established Newton's Second Law as our guiding principle (F = ma). Now, let's actually crunch the numbers and figure out the acceleration in our scenario. We know the force (F) is 30N and the mass (m) is 5kg. To find the acceleration (a), we need to rearrange the formula, making it a = F / m. This rearrangement is a simple yet crucial step in solving the problem. It’s a testament to the power of algebraic manipulation in physics, allowing us to isolate the variable we’re interested in.

Now, let's plug in those values: a = 30N / 5kg. Doing the division, we get a = 6 m/s². This is a really important result! It tells us that the body is accelerating at a rate of 6 meters per second squared. Think about what that means: every second, the body's velocity is increasing by 6 meters per second. This constant acceleration is what will ultimately lead to the body's final velocity after 5 seconds. This understanding of acceleration as a rate of change of velocity is fundamental to grasping kinematics and the motion of objects. It’s also a key concept in many other areas of physics, such as understanding gravity and the motion of projectiles. So, we've now quantified how the force is affecting the body's motion, and we're ready to move on to the final step: calculating the velocity after 5 seconds.

Finding the Final Velocity: Kinematics to the Rescue

Now that we've successfully calculated the acceleration (a = 6 m/s²), we're in the home stretch! Our next task is to determine the body's velocity after 5 seconds. To do this, we'll turn to the world of kinematics, which is essentially the study of motion. More specifically, we'll use one of the fundamental kinematic equations that relates initial velocity, final velocity, acceleration, and time. This equation is a powerful tool that allows us to predict the velocity of an object at any given time, provided we know its initial velocity, acceleration, and the time elapsed.

The kinematic equation we need is: v = u + at, where:

• v is the final velocity (what we want to find)
• u is the initial velocity
• a is the acceleration
• t is the time

Remember, the body starts at rest, so its initial velocity (u) is 0 m/s. We've already calculated the acceleration (a) as 6 m/s², and we're interested in the velocity after t = 5s. Let's plug these values into the equation: v = 0 + (6 m/s²) * (5 s). Performing the multiplication, we get v = 30 m/s. And there you have it! The final velocity of the body after 5 seconds is 30 meters per second. This is a significant speed, and it's a direct result of the constant force acting on the body over time. We've successfully used physics principles and equations to solve this problem, and hopefully, you've gained a better understanding of how forces affect motion. Physics can be pretty awesome, guys!

Putting It All Together: The Solution in a Nutshell

Okay, let's quickly recap what we've done and nail down the final answer. We started with a 5kg body at rest, subjected to a constant force of 30N. Our mission was to find its velocity after 5 seconds. Using Newton's Second Law (F = ma), we first calculated the acceleration: a = F / m = 30N / 5kg = 6 m/s². This was a crucial step, as it allowed us to quantify how the force was changing the body's motion.

Then, we employed a kinematic equation, v = u + at, to determine the final velocity. Plugging in the values we knew (u = 0 m/s, a = 6 m/s², t = 5s), we arrived at our final answer: v = 30 m/s. This means that after 5 seconds, the body is moving at a speed of 30 meters per second. This entire process demonstrates the power of physics in predicting and explaining motion. We've seen how force, mass, acceleration, and time are all interconnected, and how we can use mathematical equations to describe these relationships. So, the final answer to our problem is 30 m/s. Great job, guys, for following along! I hope this explanation has made the problem clear and understandable.

Final Answer

The velocity of the body after 5 seconds is 30 m/s.