Describing and Measuring Motion/Acceleration Study Guide

7th Grade: Describing and Measuring Motion/Acceleration

MFE 1:1 • Essential Questions

  • When is an object in motion?

  • How do you know an object’s speed and velocity?

  • How can you graph motion?

MFE 1:3 • Essential Questions

  • What kind of motion does acceleration refer to?

  • How is acceleration calculated?

  • What graphs can be used to analyze the motion of an accelerating object?

Definitions

Speed

  • Definition: Change in distance over a specific amount of time.

  • Formula:
    ext{Speed} = rac{ ext{distance}}{ ext{time}}

Average Speed

  • Definition: An average of all speeds over a given time.

  • Formula:
    ext{Average Speed} = rac{ ext{total distance}}{ ext{total time}}

Velocity

  • Definition: Change in distance over a specific amount of time with direction.

  • Formula:
    ext{Velocity} = rac{ ext{change in distance}}{ ext{time}}

Acceleration

  • Definition: Change in speed or velocity over a specific amount of time; involves speeding up, slowing down, or changing direction.

  • Formula:
    ext{Acceleration} = rac{ ext{speed}}{ ext{time}}

Units of Measurement

Speed Units

  • Measured in units of distance per time.

  • Examples:

    • Miles per hour (mi/hr)

    • Meters per second (m/s)

    • Kilometers per hour (km/hr)

Velocity Units

  • Measured in units of distance per time plus direction.

  • Examples:

    • Miles per hour north (mi/hr north)

    • Meters per second up (m/s up)

    • Kilometers per hour right (km/hr right)

Acceleration Units

  • Measured in units of speed per time.

  • Examples:

    • Miles per hour per hour (mi/hr/hr or mi/hr²)

    • Meters per second per second (m/s/s or m/s²)

    • Kilometers per hour per hour (km/hr/hr or km/hr²)

Speed Calculations

Speed Example Problem

  • A baseball is thrown a distance of 60 feet in 0.5 seconds.

  • Calculation:
    ext{Speed} = rac{60 ext{ ft}}{0.5 ext{ sec}} = 120 ext{ ft/sec}

Average Speed Example Problem

  • Archie’s running times and distances:

    • At St. Michael: 15.5 minutes for 2.0 miles

    • At St. Mary Magdalene: 13.5 minutes for 1.5 miles

    • At Home: 14.0 minutes for 1.75 miles

  • Total calculations:
    ext{Total Distance} = 2.0 ext{ mi} + 1.5 ext{ mi} + 1.75 ext{ mi} = 5.25 ext{ mi}
    ext{Total Time} = 15.5 ext{ min} + 13.5 ext{ min} + 14.0 ext{ min} = 43 ext{ min}

  • Average Speed Calculation:
    ext{Average Speed} = rac{5.25 ext{ mi}}{43 ext{ min}}
    eq 0.12 ext{ mi/min}

Velocity Calculations

Velocity Example Problem #1

  • Orla is missing for 10 minutes. Mrs. Yonkovit travels west on Leesville Road and finds her 2 miles away from the house.

  • Calculation:
    ext{Velocity} = rac{2 ext{ mi}}{10 ext{ min}} ext{ west} = 0.2 ext{ mi/min west}

Velocity Example Problem #2

  • Mrs. Yonkovit flies from Raleigh, NC to Detroit, MI (distance = 501 miles, time = 1.75 hours).

  • Calculation:
    ext{Velocity} = rac{501 ext{ mi}}{1.75 ext{ hours}} ext{ north} = 286.3 ext{ mi/hr north}

Acceleration Calculations

Acceleration Definition

  • Definition: Change in speed or velocity over a specific amount of time

Acceleration Formula

  • Formula:
    ext{Acceleration} = rac{ ext{Speed}}{ ext{Time}}

Example Units of Acceleration

  • Example:

    • Acceleration of 5 m/s² means that the speed increases by 5 meters per second every second.

Concepts Related to Motion

Center of Mass

  • Definition: The point at which an object can be balanced.

  • Importance: An object’s center of mass affects its motion greatly; in space, objects orbiting each other have a center of mass referred to as a barycenter.

    Think About It Questions

  • Compare and contrast speed and velocity:

    • Alike: Both involve distance over time.

    • Different: Velocity includes direction while speed does not.

  • Consider how mass and acceleration affect the force involved in a car crash.