Power Calculation: Force Of 50N Over 5 Seconds

Hey everyone! Let's dive into an exciting physics problem where we'll calculate the power developed by a force acting on a car. This is a classic example of how forces and motion intertwine, and understanding the concepts here can be super useful in everyday life, like figuring out how engines work or even how much energy it takes to push a grocery cart. So, buckle up, and let's get started!

Problem Breakdown: Force, Time, and Power

Okay, so here's the scenario: imagine a car being pushed with a force, let's call it F, of 50 Newtons (N). Now, this force is applied for a duration of 5 seconds. The question we need to answer is: what is the power developed by this force, F? We're given a few options, ranging from 10 Watts (W) to 50 W, and our mission is to find the correct one. To crack this problem, we'll need to remember the relationship between force, work, distance, and power. It might seem a bit complex at first, but trust me, it's like piecing together a puzzle, and the solution is incredibly satisfying. We'll break it down step by step, making sure everyone's on board. So, let's keep our thinking caps on and explore the physics behind this!

Understanding the Fundamentals

Before we jump into calculations, let's make sure we're all on the same page with some key concepts. First, what exactly is power? In physics, power is the rate at which work is done, or the rate at which energy is transferred. Think of it this way: a powerful engine can do a lot of work in a short amount of time. The unit of power is the Watt (W), named after James Watt, the famous inventor who significantly improved the steam engine. One Watt is defined as one Joule of energy per second (1 W = 1 J/s). Now, what about work? Work, in physics terms, is done when a force causes an object to move a certain distance. It's not just about applying a force; the object has to actually move for work to be done. The formula for work is simple: Work (W) = Force (F) × Distance (d). So, a larger force or a greater distance means more work is done. Lastly, let's talk about force itself. Force is simply a push or a pull that can cause an object to accelerate, change direction, or deform. In our problem, the force is what's causing the car to move, and it's the starting point for calculating the power developed. With these concepts in our toolkit, we're ready to tackle the problem head-on!

Connecting the Dots: From Force and Time to Power

Now that we've refreshed our understanding of the basics, let's figure out how to connect the given information—force and time—to find the power. The tricky part here is that we don't have the distance the car traveled. But don't worry, we can still solve this! We need to think about how force and time relate to power, even without knowing the distance directly. Remember, power is the rate at which work is done, and work is force times distance. So, if we can find a way to express power in terms of force and time, we're golden. Here's where the concept of velocity comes in handy. Velocity is the rate of change of displacement, or in simpler terms, how fast something is moving and in what direction. If we assume the force is constant and the car is moving in a straight line, we can relate the distance traveled to the velocity and time. The average power can then be expressed as the product of the force and the average velocity. This is a crucial step, as it allows us to bridge the gap between the information we have (force and time) and what we need to find (power). So, let's keep this idea in mind as we move towards the calculation phase.

Solving the Puzzle: Calculating the Power

Alright, let's get down to the nitty-gritty and calculate the power developed by the force. This is where the math comes into play, but don't worry, we'll take it step by step. We know the force (F) is 50 N, and the time (t) is 5 seconds. What we need is a formula that connects these to power (P). As we discussed earlier, power is the rate at which work is done, and work is force times distance. So, P = Work / time. But we don't have the distance! This is where we need to think a bit creatively. We can use the relationship between work, force, and velocity. The formula we're going to use is P = F × v, where v is the average velocity. Now, we still don't know the velocity directly, but we can make an assumption to simplify things. Let's assume the car starts from rest and accelerates uniformly under the influence of the force. This means the average velocity will be half the final velocity. To find the final velocity, we'd typically need more information, like the mass of the car and the acceleration. However, since we're given multiple-choice options, we can work backward from those options to see which one makes sense. This is a common strategy in physics problems, and it can be a lifesaver when you're stuck. So, let's start by trying out the answer choices and see which one fits the equation P = F × v.

Working Backwards: Testing the Options

Okay, guys, let's put on our detective hats and work backward from the answer choices to see which one fits the bill. Remember, we're looking for the power developed by the 50 N force, and we have options ranging from 10 W to 50 W. Our formula is P = F × v, where P is power, F is force (50 N), and v is the average velocity. Let's start with option (a), 10 W. If the power is 10 W, then we can rearrange the formula to find the velocity: v = P / F = 10 W / 50 N = 0.2 m/s. This means the car would have an average velocity of 0.2 meters per second. Now, does this sound reasonable for a car being pushed for 5 seconds? It seems a bit slow, but let's keep it in mind. Next, let's try option (b), 25 W. Using the same formula, v = P / F = 25 W / 50 N = 0.5 m/s. This is a bit faster, but still not very high. Let's move on to option (c), 30 W. The velocity would be v = P / F = 30 W / 50 N = 0.6 m/s. Getting faster! Option (d), 40 W, gives us v = P / F = 40 W / 50 N = 0.8 m/s. And finally, option (e), 50 W, results in v = P / F = 50 W / 50 N = 1 m/s. Now, we need to think about which of these velocities makes the most sense in the context of the problem. A velocity of 1 m/s might be more realistic for a car being pushed for 5 seconds. So, let's see if this fits our understanding of the physics involved. We're getting closer to cracking this!

The Final Deduction: Finding the Right Fit

Alright, let's put all the pieces together and make our final deduction. We've calculated the average velocities corresponding to each power option, and we've seen that a higher power leads to a higher velocity. Now, we need to consider which of these scenarios is most physically plausible. Remember, we've assumed that the car starts from rest and accelerates uniformly. If we go with the highest power option, 50 W, we get an average velocity of 1 m/s. This seems like a reasonable speed for a car being pushed for 5 seconds with a force of 50 N. The lower power options, like 10 W or 25 W, would result in much slower velocities, which might not be as realistic. To be absolutely sure, we could also consider the work done by the force and the kinetic energy gained by the car. The work done is given by Work = Force × Distance, and the kinetic energy is given by KE = 0.5 × mass × velocity^2. If we knew the mass of the car, we could calculate the distance traveled and the kinetic energy, and then compare them to the work done. However, since we don't have the mass, we have to rely on our understanding of the relationship between power, force, and velocity. Based on our analysis, the most likely answer is 50 W. It's the highest power option, and it results in a velocity that seems reasonable for the given force and time. So, let's go with option (e) as our final answer!

The Verdict: Power Developed by the Force

So, drumroll, please… The answer to the question, "What is the power developed by the force F of 50 N acting on the car for 5 seconds?" is likely (e) 50 W. We arrived at this conclusion by understanding the fundamental concepts of power, work, force, and velocity. We used the formula P = F × v to relate power to force and average velocity, and we worked backward from the answer choices to find the velocity that made the most sense. While we made some assumptions along the way, like uniform acceleration and starting from rest, this approach allowed us to solve the problem effectively. Remember, guys, physics problems are often like puzzles, and the key is to break them down into smaller steps and use the information you have to find the missing pieces. I hope this explanation has been helpful, and keep exploring the fascinating world of physics!