Physics 1600 3 Kinematics in one dimension

from Physics 1600 Review Plan Physics 1600 3 Kinematics in one dimension

• 3.1 Foundations … … … … … … … … … . . 69
• $x(t)=x(t_0)+{\int }_{t_0}^{t}d{t}^{\prime }v(t^{\prime })$, and $v(t)=v(t_0)+{\int }_{t_0}^{t}d{t}^{\prime }a(t^{\prime })$ - That’s right, it’s basic. - In high school physics, we used to write $x=v(t-t_0)$ instead of the integral. - ==However, that only works when v is constant and x(t_0) = 0==(blu3mo) - Alternatively, we can define the average velocity as $〈v〉=\frac{1}{\Delta t}{\int }_{t_0}^{t}d{t}^{\prime }v(t^{\prime })$, and then we can say $x=〈v〉\Delta t$. - So, it’s important to be aware of the limits of definite integrals. - It’s true that we have been doing math somewhat vaguely until now. - In fact, if we handle the lower limit carelessly in a first-order differential equation, we can make mistakes(blu3mo)(blu3mo)
• 3.2 One-dimensional kinematics: examples … … … … . . 71
• 3.2.1 Constant acceleration … … … … … … . . 71
  • $y=y_0+v_{0}t-\frac{1}{2}g{t}^2$
    • It’s important to be aware that this is the result of integration.
• 3.2.2 Oscillating acceleration … … … … … … . 73
• 3.2.3 Drag acceleration (linear) … … … … … . . 75
  • When a = -g - bv, there is a v where a = 0 → we can understand that there is a terminal velocity(blu3mo)(blu3mo)
• 3.2.4 Drag acceleration (squared) … … … … … . 78
• 3.2.5 Instantaneous changes in velocity … … … … . 82
• 3.3 Second-order differential equations of motion … … … . 85
  • We want to solve the form a = f(x), but it’s generally impossible.
    • There is something called the Energy method.
    • So, we have no choice but to try and get the equation by trial and error.
      • It can be done if it’s in the form a = ±kx.
• 3.3.1 Negative form, simple harmonic motion … … … 86
  • It only becomes SHM when the initial displacement/velocity is 0.
• 3.3.2 Positive form … … … … … … … … . 89
• 3.3.3 Uniqueness of solutions to linear second-order equation of motion … … … … … … … … … 91
• 3.3.4 Non-homogeneous linear second-order equation of motion 92