7th Grade Science - Motion and Graphing

Mathematical Relationships

  • B³ = CD + DA

  • B³ = (D - C imes ext{sin}(B))

  • B imes D² - 3A imes ext{cos}(B²) + A imes ext{sin}(B)

  • B³D - 4A imes ext{cos}(B²) + C imes ext{sin}(B)

  • C³ - A² - 3 imes ext{cos}(B)

Motion

Essential Questions

  • Can you measure and graph changes in motion?

  • Can you interpret an object’s motion from a graph?

  • Can you describe the characteristics of a motion graph?

Importance of Graphs in Motion

  • Graphs help make motion easier to picture and understand.

  • Lines on a graph represent an object in motion.

  • A typical speed graph will depict:

    • Distance (Position) on the y-axis

    • Time on the x-axis

Speed Graphs

Constant Speed

  • When the speed of an object remains the same, it does not increase or decrease.

  • Formula: Speed = distance / time

  • Examples:

    • 20 km / 20 minutes = 1 km/minute

    • 40 km / 40 minutes = 1 km/minute

    • 60 km / 60 minutes = 1 km/minute

  • Constant speed is represented by a straight diagonal line.

Stopped or No Speed

  • An object at rest holds the following characteristics:

    • Example: Stopping at McDonald's for lunch during a car trip.

    • Time changes, but distance remains constant.

  • Stopped is represented by a straight horizontal line on a speed graph.

Understanding Speed Graphs

  • Question: Looking at a speed graph, how can one determine if an object is moving at a constant speed or is not moving at all?

Velocity

  • Definition: Velocity is speed in a given direction.

  • Graph Interpretation:

    • Line A is moving away from point 0 (the origin).

    • Line B is moving back to point 0 (the origin).

Acceleration

Definition

  • Acceleration is defined as the change in speed or velocity over a specific amount of time.

  • On a speed graph, acceleration is represented by a curved line.

    • Observation: The steeper the incline, the faster the acceleration.

Acceleration Graphs

  • In a typical acceleration graph:

    • y-axis: Speed or velocity

    • x-axis: Time

    • Lines on the graph represent an object’s acceleration.

Constant Velocity

  • When the velocity of an object remains the same, its rate of change does not increase or decrease.

    • For example:

    • 10 m/s at 1 second

    • 10 m/s at 2 seconds

    • 10 m/s at 3 seconds

  • Constant velocity is represented by a straight horizontal line on an acceleration graph.

Constant Acceleration

  • Constant acceleration is represented at any point on the line as follows:

    • 4 m/s² at 1 sec

    • 4 m/s² at 2 sec

    • Observation: The steeper the slope, the greater the acceleration.

  • Constant acceleration is depicted as a straight diagonal line on an acceleration graph.

Changing Acceleration

  • A curved line signifies that acceleration is not constant.

    • Example: A car starts moving slowly and gradually increases its speed.

    • Observation: The steeper the line, the greater the rate of acceleration.

  • Changing acceleration is represented by a curved line on an acceleration graph.