Part 1: Motion Quantities

Overview of Motion Quantities

1. Motion quantities refer to measurable characteristics of an object's movement, including but not limited to speed, distance, acceleration, and time.

2. Understanding these quantities is essential for analyzing physical movements in various contexts, such as sports or transportation.

Example Calculations

Example 1: Speed Calculation of a Runner

• Scenario: A friend goes for a run and returns after 2 hours, having traveled a distance of 5 miles.

• Speed Calculation:

  • Speed (in mph) = Total Distance / Total Time

  • Thus, Speed = $rac{5 ext{ miles}}{2 ext{ hours}} = 2.5 ext{ mph}$

  • Question: Did they really run the entire time?

  • Determination: To answer, consider whether the distance suggests a running pace and if factors like stops are accounted for.

Example 2: Student Travel Speed

• Scenario: Use a navigation app to find the distance traveled to school and estimate the time taken.

• Speed Calculation:

  • Example Inputs: Distance = D miles, Time = T hours.

  • Speed in mph = $rac{D}{T}$ and in m/s = $rac{D imes 1609.34}{T imes 3600}$.

Example 3: Speed from Traffic Light Observation

• Scenario: You observe traveling from 20 ft in front of a traffic light to 10 ft past it over 1 second.

• Distance Traveled: 20 ft + 10 ft = 30 ft

• Speed Calculation:

  • Convert to meters: 30 ext{ ft} imes 0.3048 ext{ m/ft} \
    ightarrow 9.144 ext{ m}

  • Speed (in m/s) = $rac{9.144 ext{ m}}{1 ext{ sec}} = 9.144 ext{ m/s}$

  • Convert to mph: $9.144 ext{ m/s} imes 2.23694 = 20.5 ext{ mph}$

Example 4: Speed from Another Traffic Light Observation

• Scenario: You travel from 110 ft in front to 20 ft in front of a traffic light in 1.5 seconds.

• Distance Traveled: 110 ft - 20 ft = 90 ft

• Speed Calculation:

  • Convert to meters: $90 ext{ ft} imes 0.3048 ext{ m/ft} = 27.432 ext{ m}$

  • Speed (in m/s) = $rac{27.432 ext{ m}}{1.5 ext{ sec}} = 18.288 ext{ m/s}$

  • Convert to mph: $18.288 ext{ m/s} imes 2.23694 = 40.9 ext{ mph}$

Example 5: Trip to Mail a Bill

• Scenario: Drive 2 miles to a mailbox, 3 miles to a post office, and 4 miles home in 30 minutes total.

• Total Distance: 2 miles + 3 miles + 4 miles = 9 miles

• Total Time: 30 minutes = 0.5 hours.

• Speed Calculation:

  • Speed (in mph) = $rac{9 ext{ miles}}{0.5 ext{ hours}} = 18 ext{ mph}$

  • Convert to m/s:
    $18 ext{ mph} imes rac{0.44704 ext{ m/s}}{1 ext{ mph}} = 8.058 ext{ m/s}$

Example 6: Acceleration of Tesla Model S

• Scenario: The highest performance Tesla Model S goes from 0 mph to 60 mph in 2 seconds.

• Acceleration Calculation:

  • Convert 60 mph to m/s: $60 ext{ mph} imes 0.44704 = 26.8224 ext{ m/s}$

  • Acceleration (in m/s²) = $rac{ ext{final speed} - ext{initial speed}}{ ext{time}} = rac{26.8224 ext{ m/s} - 0}{2 ext{ s}} = 13.4112 ext{ m/s}²$

Example 7: Free Fall and Projectile Motion

• Concept: Objects in free fall near Earth's surface experience an acceleration of approximately $-9.8 ext{ m/s}²$ (downward).

• a. Baseball Thrown Upwards:

  • Initial speed = 80 mph.

  • Convert to m/s: $80 ext{ mph} imes 0.44704 = 35.7632 ext{ m/s}$

  • Speed after 2 seconds = $35.7632 ext{ m/s} - (9.8 ext{ m/s}² imes 2 ext{ s}) = 35.7632 ext{ m/s} - 19.6 ext{ m/s} = 16.1632 ext{ m/s}$

• b. Penny Dropped from Height:

  • Time of fall = 3 seconds

  • Final velocity before hitting ground can be calculated using:

  • $v = u + at$, where

  • $u = 0 ext{ (initial velocity)}, a = -9.8 ext{ m/s}², t = 3 ext{ s}$

  • Final speed = $0 + (-9.8 ext{ m/s}² imes 3) = -29.4 ext{ m/s}$ (just before impact).

Conclusion

• Understanding motion quantities allows for the analysis of various physical scenarios and aids in practical applications such as calculating speeds and understanding acceleration in different contexts.