সরল ছন্দিত গতি সম্পন্ন একটি কণার গতির সমীকরণ $y=10 \sin (12t-\pi /3)$ যেখানে y এর একক মিটার, t এর একক সেকেন্ড এবং দশা একক রেডিয়েন । 6.28 sec সময়ে বস্তুটির ত্বরন কত ?

The given answer is correct because it effectively calculates the acceleration of the particle at a specific time based on the motion equation provided. In simple harmonic motion, the acceleration can be determined by taking the second derivative of the position equation with respect to time.

Here are the steps that lead to the answer:

    
1. Identify the equation: The position of the particle is given by y = 10 sin(12t - π/3).
    
2. Find the first derivative: Differentiate this equation with respect to time t to find the velocity (v).
    
3. Find the second derivative: Differentiate the velocity function to find the acceleration (a).
    
4. Substitute the time: Evaluate the acceleration at t = 6.28 seconds.

After performing these calculations, you arrive at the result of 1.25 k m/s², which corresponds to the answer given in the options. Hence, the answer 1.25 k m/s² accurately represents the acceleration of the particle at the specified time.

AI-এর ব্যাখ্যায় ভুল থাকতে পারে।