Hey guys! Ever wondered about the third equation of motion? If you're diving into the world of physics, especially in Hindi, this is a super important concept to grasp. It's not just about memorizing a formula; it's about understanding how things move and why. We're going to break down the third equation of motion in Hindi, covering everything from its formula and derivation to real-world applications. Let's get started!

Understanding the Third Equation of Motion: Basics

Alright, so what exactly is the third equation of motion? Well, it's a fundamental equation in classical mechanics that relates an object's final velocity (v), initial velocity (u), acceleration (a), and the displacement (s) or distance it travels. Unlike the first two equations, which often involve time (t), the third equation provides a direct relationship between these kinematic variables without explicitly considering time. It's super handy when you don't know the time or don't need to calculate it directly.

The equation itself is: v² = u² + 2as. Simple, right? But what does each term mean?

• v: Final velocity - The speed and direction of the object at the end of its motion (in m/s).
• u: Initial velocity - The speed and direction of the object at the beginning of its motion (in m/s).
• a: Acceleration - The rate at which the velocity changes (in m/s²). This can be positive (speeding up) or negative (slowing down).
• s: Displacement - The change in position of the object (in meters). Note: Displacement is a vector quantity; this is the magnitude of the displacement.

So, this third equation of motion helps us find the final velocity of an object if we know its initial velocity, acceleration, and the distance it covered, without considering the time taken. It's a key tool for solving a bunch of physics problems, from simple calculations to more complex scenarios. In Hindi, it's often written as: v² = u² + 2as (व² = उ² + २अस्), where व is v, उ is u, अ is a, and स् is s. Keep in mind that understanding each component is crucial for applying the formula correctly.

Deriving the Third Equation of Motion: Step-by-Step

Let's get into the derivation of the third equation of motion! It’s actually pretty straightforward, and knowing how it's derived helps you understand why the formula works. We'll start with the first two equations of motion and use them to get to our final equation. Here’s how we can derive the equation step-by-step:

1. Start with the First Equation of Motion: The first equation of motion is: v = u + at. This equation tells us the final velocity (v) is equal to the initial velocity (u) plus the product of acceleration (a) and time (t).

2. Rearrange the First Equation to Solve for Time (t): We need to express time (t) in terms of the other variables. Rearranging the first equation, we get: t = (v - u) / a

3. Use the Second Equation of Motion: The second equation of motion is: s = ut + (1/2)at². This equation relates displacement (s) to initial velocity (u), time (t), and acceleration (a).

4. Substitute the Value of t: Now, substitute the value of t from the first equation (rearranged) into the second equation: s = u[(v - u) / a] + (1/2)a[(v - u) / a]²

5. Simplify the Equation: Let's simplify and solve for s. This might involve some algebraic manipulation: s = (uv - u²) / a + (1/2)a(v² - 2uv + u²) / a² s = (uv - u²) / a + (v² - 2uv + u²) / (2a)

6. Multiply by 2a to eliminate the denominator: Multiplying throughout by 2a yields: 2as = 2uv - 2u² + v² - 2uv + u²

7. Rearrange the terms to get the third equation: Combine like terms and rearrange to get: 2as = v² - u²

8. Finally: v² = u² + 2as

And there you have it! The third equation of motion derived from the first two. This derivation shows you how the relationships between velocity, acceleration, and displacement work together.

Applications of the Third Equation of Motion: Examples in Hindi

The third equation of motion isn't just a formula; it's a powerful tool with many real-world applications. It's used everywhere, from calculating the speed of a car to analyzing the motion of a ball thrown in the air. Let's see some examples in Hindi to get a clearer picture:

• Car Braking: Imagine a car is slowing down. You know the initial speed, the deceleration (negative acceleration), and the distance it travels while braking. The third equation helps you find the final velocity (which, ideally, is zero).

  • Hindi Example: यदि एक कार 20 m/s की गति से चल रही है और 50 मीटर की दूरी पर रुकती है, और उसका मंदन -2 m/s² है, तो v² = u² + 2as का उपयोग करके आप इसकी अंतिम गति (0 m/s) की गणना कर सकते हैं.

• Projectile Motion: When you throw a ball, the third equation of motion can help calculate the final velocity of the ball just before it hits the ground, given the initial velocity and the height it was thrown from (acceleration due to gravity is the acceleration).

  • Hindi Example: एक गेंद को 10 m/s की प्रारंभिक गति से ऊपर फेंका जाता है, और गुरुत्वाकर्षण के कारण त्वरण -9.8 m/s² है। आप गेंद की जमीन पर गिरने से ठीक पहले की अंतिम गति की गणना कर सकते हैं।

• Skydivers: Considering the air resistance, the equation can approximate the final velocity of a skydiver after a certain distance of freefall, knowing the initial velocity (which is zero at the start of the jump) and the acceleration due to gravity.

  • Hindi Example: एक स्काईडाइवर बिना प्रारंभिक गति के छलांग लगाता है। 9.8 m/s² के गुरुत्वाकर्षण के त्वरण के साथ, और एक निश्चित दूरी के बाद, आप v² = u² + 2as का उपयोग करके उसकी अंतिम गति की गणना कर सकते हैं।

• Roller Coasters: Designing roller coasters involves applying this equation to ensure that the cars reach a specific speed at various points, considering the change in height and acceleration due to gravity.

  • Hindi Example: एक रोलर कोस्टर की गति की योजना बनाने के लिए, आप उसकी ऊँचाई में परिवर्तन और गुरुत्वाकर्षण के कारण त्वरण का उपयोग करके विभिन्न बिंदुओं पर इसकी गति की गणना करते हैं।

These are just a few examples. The third equation of motion is also essential in fields like engineering, sports science, and any area where motion analysis is critical. Recognizing how and where to apply this equation is a major step in understanding physics.

Solving Problems with the Third Equation of Motion: Tips & Tricks

Okay, guys, ready to dive into some problem-solving? Using the third equation of motion can seem easy, but here are some tips and tricks to make sure you get it right every time:

• Identify the Knowns and Unknowns: Always start by writing down what you know (initial velocity, acceleration, displacement) and what you need to find (final velocity). This helps you pick the right equation.

• Units, Units, Units! Make sure all your units are consistent. For example, if acceleration is in m/s², then velocity should be in m/s and displacement in meters. If the units are mixed, you must convert them.

• Direction Matters: Displacement, velocity, and acceleration are all vector quantities. This means they have direction. Pay attention to whether the motion is along a straight line and whether things are speeding up or slowing down. Consider signs (+ or -) to represent direction.

• Understand the Assumptions: The equation works best with constant acceleration. Make sure the acceleration remains constant throughout the motion. If the acceleration changes, you might need to split the problem into different parts.

• Practice Makes Perfect: The more problems you solve, the better you’ll get. Try different scenarios, and don't be afraid to make mistakes. Mistakes are how we learn!

• Use Diagrams: Drawing a diagram can often help you visualize the problem. Sketching the situation can help you to understand the direction of movement, the initial and final states, and the various parameters involved. This will help you identify the values to be used.

• Check Your Answer: After solving, always check if your answer makes sense. Does the final velocity seem reasonable based on the scenario? Is it a positive or negative value, and does that align with the problem's physical context?

By following these tips, you can confidently use the third equation of motion to solve a variety of physics problems.

Common Mistakes to Avoid

Hey, we've all been there! Making mistakes is part of learning. To help you out, let's talk about some common pitfalls to avoid when using the third equation of motion:

• Confusing Variables: Make sure you correctly identify u (initial velocity) and v (final velocity). It's easy to mix them up, especially if the problem is worded in a tricky way. Double-check before you start plugging in values.

• Sign Errors: Pay close attention to the signs (positive or negative) of acceleration and displacement. Acceleration is negative when an object slows down (deceleration). Displacement is positive when moving in the positive direction and negative when moving in the negative direction. The most common mistake made is in the sign of acceleration. Always be careful about its direction.

• Incorrect Units: As we said before, unit consistency is critical. Make sure all units are in the same system (e.g., SI units: meters, seconds, m/s²). If they are not, convert them before you start calculations.

• Ignoring the Context: Always think about the physical context of the problem. Does your answer make sense? A negative final velocity doesn't make sense if an object is always moving forward. Always consider the real-world implications.

• Misunderstanding Displacement: Remember that displacement is not the same as distance traveled. Displacement is the change in position. In a round trip, the total displacement might be zero, even if the object moved a significant distance. Focus on the start and end positions.

• Assuming Constant Acceleration: The third equation of motion is applicable only if acceleration is constant. If the acceleration is not constant, you can't use it directly. If the acceleration changes, you may need to break the motion into separate parts where acceleration is constant.

Avoiding these common mistakes will make you a better problem-solver and help you master the third equation of motion.

Conclusion: Mastering the Third Equation of Motion

Alright, folks, we've covered a lot today! You now have a solid understanding of the third equation of motion in Hindi, its formula (v² = u² + 2as), its derivation, and its applications. You know how to solve problems, avoid common mistakes, and apply this powerful tool to real-world scenarios. Remember, it's all about practice and understanding the concepts.

So, go out there, solve some problems, and keep exploring the amazing world of physics. Good luck, and keep learning! If you have any questions, feel free to ask. Happy calculating!