Calculating Velocity From Momentum And Mass A Physics Problem

Hey everyone! Today, we're diving into a classic physics problem: figuring out the velocity of an object given its momentum and mass. It's a fundamental concept, and understanding it can help you grasp a lot about how objects move. So, let's get started!

The Momentum Equation: Unlocking the Secrets of Motion

Momentum, at its core, is a measure of how much "oomph" an object has in its motion. A heavier object moving at the same speed as a lighter one will have more momentum. Similarly, an object moving faster will have more momentum than the same object moving slower. This brings us to the momentum equation, which is the key to solving our problem. This equation beautifully encapsulates this relationship, stating that momentum (p) is equal to the mass (m) of the object multiplied by its velocity (v). Mathematically, we express this as:

p = m * v

Where:

• p represents momentum, typically measured in kilogram-meters per second (kg-m/s).
• m represents mass, typically measured in kilograms (kg).
• v represents velocity, typically measured in meters per second (m/s).

This equation is your bread and butter when dealing with momentum-related problems. It's simple, yet incredibly powerful, allowing us to connect these three crucial aspects of an object's motion. In our case, we're given the momentum and the mass, and our mission, should we choose to accept it (and we do!), is to find the velocity. We already know the momentum, which is a robust 4,000 kg-m/s, and the mass, a hefty 115 kg. What we are searching for, the missing piece of our puzzle, is the velocity. To find this missing piece, we're going to need to do a little algebraic maneuvering. Don't worry; it's easier than it sounds! We're going to rearrange our momentum equation to isolate velocity on one side. This will give us a new equation that we can plug our known values into and voilà, the velocity will be revealed!

Rearranging the Equation: Isolating Velocity

To find the velocity, we need to rearrange the momentum equation. Remember, our goal is to get 'v' all by itself on one side of the equation. Currently, it's multiplied by 'm' (mass). To undo this multiplication, we'll perform the inverse operation: division. We'll divide both sides of the equation by 'm'. This ensures that the equation remains balanced – a golden rule in algebra! Performing this division, we get:

p / m = (m * v) / m

On the right side, the 'm' in the numerator and the 'm' in the denominator cancel each other out, leaving us with just 'v'. This is exactly what we wanted!

Our rearranged equation now looks like this:

v = p / m

This equation is our new best friend. It tells us that the velocity of an object is equal to its momentum divided by its mass. Now, we have a clear path forward. We know the values for 'p' (momentum) and 'm' (mass), so we can simply plug them into this equation and calculate 'v' (velocity). It's like having the recipe for success; we have all the ingredients, and now it's time to cook!

Plugging in the Values: Time to Calculate!

Alright, folks, let's get down to the nitty-gritty and plug in the values we have into our rearranged equation. We know the momentum (p) is 4,000 kg-m/s, and the mass (m) is 115 kg. So, let's substitute these values into our equation:

v = 4000 kg-m/s / 115 kg

Now, it's just a matter of performing the division. Grab your calculators, or if you're feeling particularly bold, you can try doing it by hand! This step is crucial because it's where we actually quantify the velocity. We're taking the abstract concepts of momentum and mass and turning them into a concrete number that represents how fast the object is moving. Think of it like translating a foreign language – we're taking the language of physics and translating it into a real-world value that we can understand and use.

When we perform the division, we get a result that represents the velocity in meters per second (m/s). This unit is important because it tells us the distance the object covers in one second. It's a standard unit for measuring speed and velocity, and it's how we typically describe the motion of objects in physics.

The Result: Velocity Revealed!

After performing the calculation, we find that:

v ≈ 34.78 m/s

But hold on! The problem asked us to round to the nearest hundredth. Lucky for us, our answer is already rounded to the nearest hundredth! This means our final answer, the velocity of the object, is approximately 34.78 meters per second. We have successfully navigated the problem, applied the momentum equation, and calculated the velocity. Give yourselves a pat on the back!

So, what does this number actually mean? Well, it tells us that the object is moving at a speed of roughly 34.78 meters every second. To put that into perspective, it's faster than most cars travel in city traffic! This gives us a sense of the object's motion and the magnitude of its velocity.

Conclusion: Mastering Momentum

So, we've successfully calculated the velocity of an object given its momentum and mass. We started with the fundamental momentum equation, rearranged it to solve for velocity, plugged in our values, and arrived at our answer: approximately 34.78 m/s. This problem highlights the power of the momentum equation and its ability to connect mass, velocity, and momentum. Guys, remember, physics is all about understanding these relationships and applying them to the world around us. Keep practicing, and you'll be momentum masters in no time!

Therefore, the correct answer is:

A. 34.78 m/s