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...
1. 20, 22, 23, 25, 32, 38, .... , .... , 53 a. 30 dan 42 b. 35 dan 47 c. 33 dan 41 d. 41 dan 52 e. 42 dan 54 Pembahasan : Jawaban : A 2. \( 1\frac{5}{10}, 1\frac{7}{10}, 3\frac{2}{10}, 3, 3\frac{2}{10}, 6\frac{2}{10}, 4\frac{5}{10}, 4\frac{7}{10} \), ..... , ..... a. \( 6\frac{2}{10}, 6 \) b. \( 6\frac{2}{10}, 10\frac{9}{10} \) c. \( 9\frac{2}{10}, 10\frac{9}{10} \) d. \( 9\frac{2}{10}, 6 \) e. \( 9\frac{2}{10}, 10\frac{4}{10} \) Pembahasan : Pecahan campuran diubah terlebih dahulu ke pecahan biasa: \( \frac{15}{10}, \frac{17}{10}, \frac{32}{10}, \frac{30}{10}, \frac{32}{10}, \frac{62}{10}, \frac{45}{10}, \frac{47}{10}\), .... ,.... Perhatikan deret pembilangnya : 15, 17, 30 , 32, 62, 45, 47, ..., .... Dengan demikian, polanya menjadi seperti : Maka bilangan berikutnya adalah \( \frac{92}{10}, \frac{60}{10}, \) ataun \( 9\frac{2}{10}, 6 \) Jawaban : A 3. 1, 5, 4, 3, 7, 1, 10, -1, 13, -3, ...., ..... a. 16, -...