Chapter 1: Conversion Units

Conversion of Speed from mph to m/s

• Airplane cruising speed is 650 miles per hour (mph).
• Conversion requires knowledge of standard units:
  • Length: meter (m)
  • Time: second (s)
  • Mass: kilogram (kg)
• Conversion factors:
  • 1 centimeter (cm) equals 10^-2 meters (m)
  • 1 millimeter (mm) equals 10^-3 meters (m)

Step-by-step Calculation

• To convert 650 mph to meters per second (m/s):
  • Use the conversion:
    • Multiply by the conversion factor: 1 mile = 1.609 kilometers (km)
    • Multiply by the conversion factor: 1 kilometer = 1000 meters (m)
    • Convert hours to seconds: 1 hour = 60 minutes, 1 minute = 60 seconds
• Final calculation results in: 650 mph = 290.513889 m/s

Importance of Unit Conversion

• Accurate unit conversions are critical for scientific calculations and standards.
• Understanding conversion factors helps navigate between different measurement systems efficiently.

Mechanics and Kinematics

• Mechanics combines kinematics and dynamics to study motion.
• Kinematics focuses on describing motion without considering forces affecting it.

Key Concepts in Motion

• Position: Indicates the location of an object in space, typically analyzed using a three-dimensional frame of reference.
• Speed vs. Velocity: Speed refers to how fast an object moves, while velocity includes direction.
• Acceleration: Describes whether the motion is uniform, indicating changes in velocity over time.

Position

• Example values of position can be noted as Position=4.0mPosition = 4.0 mPosition=4.0m or Position=−2.5mPosition = -2.5 mPosition=−2.5m.
• The x-coordinate, denoted as XXX, specifies the object's location on a horizontal axis.

Displacement

• Displacement is represented by the symbol Δx\Delta xΔx, calculated as the difference between final and initial positions.
• Formula: Δx=x2−x1\Delta x = x_2 - x_1Δx=x2​−x1​ where x1x_1x1​ is the initial position and x2x_2x2​ is the final position.
• Example: If T1T_1T1​ at position x1=0x_1 = 0x1​=0 m and T2T_2T2​ at position x2=4x_2 = 4x2​=4 m, then Displacement=4−0=4Displacement = 4 - 0 = 4Displacement=4−0=4 m.