T = 2π√(l/g): depends on l and g, independent of mass (gravitational and inertial mass cancel). Memory aid: 'Pendulum: T ∝ √(l/g); independent of mass for small angles'. Oscillations concept frequently tested in competitive exams.
Explanation:
Acceleration a = dv/dt = d(3t² + 2t)/dt = 6t + 2. At t = 2 s: a = 6(2) + 2 = 14 m/s². Differentiation of velocity gives instantaneous acceleration. Memory tip: a = dv/dt; for polynomial v(t), differentiate term by term. Tests calculus application in kinematics, common in advanced competitive exam questions.
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