AI-তৈরি নমুনা উত্তর
দেওয়া আছে,y = 10 sin ( 12 t − π 3 ) y = 10 \sin\left(12t - \frac{\pi}{3}\right) y = 10 sin ( 12 t − 3 π )
কণাটির বেগ,v = d y d t = 10 × 12 cos ( 12 t − π 3 ) = 120 cos ( 12 t − π 3 ) v = \frac{dy}{dt} = 10 \times 12 \cos\left(12t - \frac{\pi}{3}\right) = 120 \cos\left(12t - \frac{\pi}{3}\right) v = d t d y = 10 × 12 cos ( 12 t − 3 π ) = 120 cos ( 12 t − 3 π )
কণাটির ত্বরণ,a = d 2 y d t 2 = − 120 × 12 sin ( 12 t − π 3 ) = − 1440 sin ( 12 t − π 3 ) m/s 2 a = \frac{d^2y}{dt^2} = -120 \times 12 \sin\left(12t - \frac{\pi}{3}\right) = -1440 \sin\left(12t - \frac{\pi}{3}\right) \text{ m/s}^2 a = d t 2 d 2 y = − 120 × 12 sin ( 12 t − 3 π ) = − 1440 sin ( 12 t − 3 π ) m/s 2
এখানে, t = 6.28 s ≈ 2 π s t = 6.28 \text{ s} \approx 2\pi \text{ s} t = 6.28 s ≈ 2 π s a = − 1440 sin ( 12 × 2 π − π 3 ) a = -1440 \sin\left(12 \times 2\pi - \frac{\pi}{3}\right) a = − 1440 sin ( 12 × 2 π − 3 π ) = − 1440 sin ( 24 π − π 3 ) = -1440 \sin\left(24\pi - \frac{\pi}{3}\right) = − 1440 sin ( 24 π − 3 π ) = − 1440 ( − sin π 3 ) = -1440 \left(-\sin\frac{\pi}{3}\right) = − 1440 ( − sin 3 π ) = 1440 × 3 2 = 720 3 ≈ 1247.08 m/s 2 = 1440 \times \frac{\sqrt{3}}{2} = 720\sqrt{3} \approx 1247.08 \text{ m/s}^2 = 1440 × 2 3 = 720 3 ≈ 1247.08 m/s 2
[বিকল্পভাবে, t = 6.28 t = 6.28 t = 6.28 12 ( 6.28 ) − π 3 = 75.36 − 1.0472 = 74.3128 rad 12(6.28) - \frac{\pi}{3} = 75.36 - 1.0472 = 74.3128 \text{ rad} 12 ( 6.28 ) − 3 π = 75.36 − 1.0472 = 74.3128 rad sin ( 74.3128 rad ) ≈ − 0.87156 \sin(74.3128 \text{ rad}) \approx -0.87156 sin ( 74.3128 rad ) ≈ − 0.87156 a = − 1440 × ( − 0.87156 ) ≈ 1255.05 m/s 2 a = -1440 \times (-0.87156) \approx 1255.05 \text{ m/s}^2 a = − 1440 × ( − 0.87156 ) ≈ 1255.05 m/s 2
উত্তর: 1247.08 m/s 2 1247.08 \text{ m/s}^2 1247.08 m/s 2 1255.05 m/s 2 1255.05 \text{ m/s}^2 1255.05 m/s 2