Chapter 2: One-Dimensional Kinematics

Derived Units

  • These are units that are formed by combining base units through multiplication or division. They are not fundamental units themselves but are derived from them.

    • Area: The product of two lengths, typically measured in square meters (m^2).

    • Volume: The product of three lengths, typically measured in cubic meters (m^3).

    • Density: Mass per unit volume, measured in kilograms per cubic meter (kg/m^3).

    • Velocity: Distance per unit time, measured in meters per second (m/s).

    • Force: Mass times acceleration (kg \cdot m/s^2), also known as Newtons (N). Here, acceleration is itself a derived unit (m/s^2).

  • How might you determine the density of a solid?

    • Density= mass/volume

Standardized Units

  • These are universally accepted and defined units of measurement that provide a common reference for quantities. They are crucial for consistency in scientific, commercial, and everyday applications worldwide. The most widely adopted system of standardized units is the International System of Units (SI).

  • Examples (SI Base Units):

    • Length: Meter (m)

    • Mass: Kilogram (kg)

    • Time: Second (s)

    • Electric Current: Ampere (A)

    • Temperature: Kelvin (K)

    • Amount of Substance: Mole (mol)

    • Luminous Intensity: Candela (cd)

How do we report our answer?

  • We must use significant figures

  • Two types of numbers:

    1. Exact Numbers (part of a definition)

    2. Measured Numbers

  • The significant figures in any measurement are the digits that are known with certainty, plus one digit that is uncertain.

Precision VS Accuracy

  • Precision- Reproducibility, how close a series of measurements are to one another

  • Accuracy- How close the measured value is to the actual value

Significant Figures for Calculations

Which figures are significant?

  • All non-zero digits

  • Interior Zeroes

  • Trailing zeroes

Which figures are not significant?

  • Leading zeroes

  • Ambiguous

Mechanics

  • Kinematics- deals with the mathematical description of the motion of objects

  • Dynamics- concerned its the causes of motion

Scalar Quantities: measures or values that can be fully described with only a numerical value (magnitude)

Vector Quantities: measures or values that can be fully described by both a numerical value and a direction (require magnitude and direction)

Distance: the path length traveled from one location to another

  • distance is a scalar quantity- it is described only by a magnitude

Average Speed is the distance traveled divided by the elapsed time (in meters)

  • delta= change in

Since distance is a scalar, speed is also a scalar (as is time).

Instantaneous speed is the speed measured over a very short time span. This is what a speedometer reads.

Velocity is speed with a direction and magnitude. (Change in displacement/change in time)

  • Displacement is the vector analog (or version) of distance, and velocity is the vector analog of speed.

Average Velocity is the displacement of an object divided by the elapsed time.

Uniform Motion- motion with a constant or uniform velocity

Acceleration:

  • the rate at which velocity changes

    • average velocity= change in velocity/time to make the change

    • Acceleration means that the magnitude of the velocity of an object is changing, or its direction is, or both.

    • If the acceleration is constant, we can find the velocity as a function of time: v= Vo + at

Kinematic Equations:

  • Xf= Xi + ViT + 1/2at²

  • Vf= Vi + at

  • Vf² = Vi² + 2(a(Xf - Xi))

Constant Acceleration Equations for Free Fall:

  • Vf = Vi - get

  • Yf = Yi + VoT - 1/2gt²

  • Vf² = Vo² - 2g( Yf - Yi)