Physics 1

What is the first step in understanding physical processes?

Physical processes are observed and measured both quantitatively and qualitatively.

What does the observation step of a physical process necessarily include?

The conception and definition of appropriate quantities by which measurements may be made.

In what form is a hypothesis usually offered in physics?

In the form of a general principle or a mathematical statement of relationships between physical quantities.

What is the primary use of physical principles or relationships?

They can be used to predict the results of other similar physical processes.

What is considered the working language of physics?

Mathematics.

What specific mathematical fields are noted as necessary for mastering physics?

Analytic geometry, calculus, trigonometry, and vector analysis.

Instantanenous Acceleration

Formula: $a_x = \frac{dv_x}{dt} = \frac{d^2x}{dt^2}$

($a_x\text{ [m/s}^2\text{]}, v_x\text{ [m/s]}, t\text{ [s]}$ )

General 1D motion with differentiable $v_x(t)$

Velocity-Time Relation

$v_x = v_{0x} + a_x t$

($v_{0x}, v_x\text{ [m/s]}, a_x\text{ [m/s}^2\text{]}, t\text{ [s]}$)

Constant 1D acceleration ($a_x = const$)

Position-Time-Relation

$$x = x_0 + v_{0x}t + \frac{1}{2}a_x t^2$$

($x_0, x\text{ [m]}, v_{0x}\text{ [m/s]}, a_x\text{ [m/s}^2\text{]}, t\text{ [s]}$)

Constant 1D acceleration ($a_x = \text{const}$)

Timeless Kinematic Relation

$$v_{f}^2=v_{i}^2+2a\Delta x$$

($v_{0x}, v_x\text{ [m/s]}, a_x\text{ [m/s}^2\text{]}, \Delta x\text{ [m]}$ )

Constant 1D acceleration ($t$ unknown)

Average velocity displacment

$$\Delta x = \frac{1}{2}(v_{0x} + v_x)t$$

($\Delta x\text{ [m]}, v_{0x}, v_x\text{ [m/s]}, t\text{ [s]}$)

Constant 1D acceleration ($a_x$ unknown)

Free-Fall Kinematics ($+y$up)

$$y = y_0 + v_{0y}t - \frac{1}{2}gt^2$$

($y\text{ [m]}, v_{0y}\text{ [m/s]}, g = 9.80\text{ m/s}^2$)

Negligible air resistance near Earth surface

General Calculus Integration

$$v_x(t) = v_{0x} + \int_0^t a_x(t') dt'$$

($a_x(t)\text{ [m/s}^2\text{]}, v_x(t)\text{ [m/s]}$)

Time-dependent acceleration $a_x(t)$

Average Velocity

$$\bar{v} = \frac{\Delta x}{\Delta t} = \frac{x_f - x_i}{t_f - t_i}$$

$\bar{v} \text{ (average velocity)} \\ \Delta x \text{ (displacement)} \\ \Delta t \text{ (time interval)} \\ x_f \text{ (final position)} \\ x_i \text{ (initial position)} \\ t_f \text{ (final time)} \\ t_i \text{ (initial time)}$

Displacement

$$\Delta x=x_f-x_i$$

To find the change in position. Valid for any motion.

Average Velocity

$$v_{\text{avg}}=\frac{\Delta x}{\Delta t}$$

When displacement and elapsed time are known. Valid for any motion over a nonzero interval.