Imagine a particle of mass m, constrained to move along the x-axis, subject to some specified force F(x, t). The program of classical mechanics is to deter- mine the position of the particle at any given time: x(t). Once we know that, we can figure out the velocity (\( v=\frac{dx}{dt}\) ), the momentum (p = mv), the kinetic energy ( \( T=\frac{1}{2}mv^2 \) ), or any other dynamical variable of interest. And how do we go about determining x(t)? We apply Newton's second law: F = ma. (For conservative systems the only kind we shall consider, and, fortunately, the only kind that occur at the microscopic level---the force can be expressed as the derivative of a potential energy function, \( F=-\frac{\partial V}{\partial x} \) , and Newton's law reads \( m\frac{d^2x}{dt^2}=-\frac{\partial V}{\partial x} \) .) This, together with appropriate initial conditions (typically the position and velocity at t 0), determines x(t). Quantum mechanics approaches this same problem quite differentl...
Soal dan pembahasan bentuk pangkat - Bentuk pangkat adalah topik matematika penting dan sering diujikan dalam berbagai jenis ujian. Pemahaman aturan dasar perpangkatan penting untuk menyelesaikan soal dan pembahasan bentuk pangkat. Contoh soal dan pembahasan bilangan berpangkat membantu memperkuat pemahaman kita tentang bentuk pangkat. Soal Nomor 1. Nilai dari \( \frac{(343)^{\frac{1}{2}}-(625)^{\frac{1}{4}}}{(27)^{\frac{1}{3}}+(4)^{\frac{1}{2}}} \) adalah .... A. \( \frac{2}{5} \) B. \( \frac{2}{4} \) C. \( \frac{5}{2} \) D. 2 E. \( \frac{8}{2} \) Pembahasan : \begin{align*} \frac{(343)^{\frac{1}{2}}-(625)^{\frac{1}{4}}}{(27)^{\frac{1}{3}}+(4)^{\frac{1}{2}}} &= \frac{(7^3)^{\frac{1}{2}}-(5^4)^{\frac{1}{4}}}{(3^3)^{\frac{1}{3}}+(2^2)^{\frac{1}{2}}} \\ &= \frac{7-5}{3+2} \\ &= \frac{2}{5} \end{align*} Jawaban : A Soal Nomor 2. Bentuk sederhana dari \( \left( \frac{2^5a^{12}b^2}{2a^8b^{-2}c^{-4}} \right) \) adalah ...