Physics 20AP: Unit 1 Notes - 1D Kinematics

Fundamental Skills

• Measurement: The last digit is uncertain; the number of digits indicates precision.
• Significant Digits: Counted quantities and definitions have infinite significant digits.
• Mathematical Operations: Final solution should have as many significant digits as the measured quantity with the fewest significant digits.
• Scientific Notation: Express numbers as a value between one and ten multiplied by a power of ten.
• Unit Conversions: Use conversion factors with a value of 1 to convert units.
• Solving Equations: Simplify, isolate the variable's term, and eliminate fractions.

Describing Motion and Analyzing Uniform Motion

• Scalar vs. Vector Quantities: Scalar quantities have magnitude only; vector quantities have both magnitude and direction.
• Position $\vec{d}$: Location relative to a reference point; a vector quantity.
• Distance $d$: Length of the path traveled; a scalar quantity.
• Total Displacement $\Delta \vec{d}<em>T$: Change in position; a vector quantity calculated as $\Delta \vec{d}</em>T = \vec{d}<em>f - \vec{d}</em>i$ .
• Algebra in 1D Vector Formulas: Define a positive direction; substitute quantities accordingly.
• Analyzing Motion with Multiple ‘Legs’: Use subscripts for each leg of the motion; $\Delta \vec{d}<em>T = \Delta \vec{d}</em>1 + \Delta \vec{d}_2 + \cdots$
• Types of Motion: Simplify real motion with idealized mathematical models.
• Velocity $\vec{v}$: Rate of change of position; a vector quantity.
• Uniform Motion: Constant velocity; analyzed using $\vec{v} = \frac{\Delta \vec{d}}{t}$ .

Analyzing Uniformly Accelerated Motion

• Acceleration $\vec{a}$: Rate of change of velocity; a vector quantity.
• Accelerating Objects: Object speeds up when $\vec{a}$ and $\vec{v}$ are in the same direction and slows down when in opposite directions.
• Uniformly Accelerated Motion: Constant acceleration; use formulas such as $\vec{a} = \frac{\Delta \vec{v}}{t}$, $\Delta d = v<em>i t + \frac{1}{2} a t^2$, $\Delta d = v</em>f t - \frac{1}{2} a t^2$, $v<em>f^2 = v</em>i^2 + 2 a \Delta d$, and $\Delta d = (\frac{v<em>f + v</em>i}{2}) t$ .

Vertical Projectiles

• Projectiles: Objects moving solely under gravity's influence, with $a = 9.81 \frac{m}{s^2} \equiv g$ near Earth's surface.
• Vertical Projectiles Summary: At maximum height, $v = 0$. When initial and final positions are at the same height, $t<em>{up} = t</em>{down}$ and $v<em>{up} = -v</em>{down}$.
• Proportions: Describe variable relationships in equations to determine how changes affect each other (linear, quadratic, inverse).

Average Speed and Average Velocity

• Instantaneous vs. Average Speed/Velocity: Instantaneous speed is velocity at a moment; average speed and velocity consider the entire motion.
• Average Speed: $v<em>{avg} = \frac{d</em>{total}}{t_{total}}$
• Average Velocity: $\vec{v}<em>{avg} = \frac{\Delta \vec{d}</em>{total}}{t_{total}}$
• Measuring Velocities Using Photogates: Calculate average velocity over time intervals; for uniform motion, $\vec{v}<em>{avg} = \frac{\Delta \vec{d}}{t} = \vec{v}$; for accelerated motion, $\vec{v}</em>{avg} = \frac{\Delta \vec{d}}{t} \neq \vec{v}<em>i \neq \vec{v}</em>f$ , but for small intervals, $\vec{v}<em>{avg} \approx \vec{v}</em>{instantaneous}$ .

Graphing Motion

• Drawing Scientific Graphs: Include title, labeled axes with units, linear scales, plotted data points, and a line of best fit.
• Analyzing Position-Time Graphs: The slope gives velocity.
• Analyzing Velocity-Time Graphs: The slope gives acceleration, and the area under the curve gives displacement.