4/12 Force and Motion pt. 1

Displacement and Distance

• Displacement: Refers to the change in position of an object.
  • Always less than or equal to the distance traveled.
• Distance: Total length of the path traveled from one point to another.

Motion and Measurement

• Optic's Motion: Involves a change in position over a period of time.
• Speed:
  • Measure of how fast position changes.
  • No concern for direction
  • Formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
• Velocity:
  • Speed with direction; hence a vector quantity.
  • Formula: $\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}$

Example Scenario: Car Trip

• Imagine a car travels:
  • Distance: 35 miles (on road)
  • Displacement: 20 miles (straight line northeast from home)
  • Time Taken: 1 hour.
• Calculating Average Speed:
  • $\text{Average Speed} = \frac{35 \text{ miles}}{1 \text{ hour}} = 35 \text{ miles per hour}$
• Calculating Average Velocity:
  • $\text{Average Velocity} = \frac{20 \text{ miles}}{1 \text{ hour}} = 20 \text{ miles per hour northeast}$

Acceleration

• Definition: Measure of how quickly an object changes its velocity.
  • Involves changes in speed or direction.
  • If an object speeds up, slows down, or changes direction, it experiences acceleration.
• Calculation:
  • Formula: $\text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}}$
• Example:
  • A fast car accelerates from 0 to 60 miles per hour south in 6 seconds.
  • $\text{Acceleration} = \frac{60 - 0 \text{ mph}}{6 \text{ seconds}} = 10 \text{ miles per hour per second south}$
• SI Unit: Meters per second each second (m/s²).
  • If no direction is given, it's assumed that the object is not changing its direction.