Movement & Position Flashcards

Distance-Time Graphs

• Distance-time graphs illustrate the distance an object travels in a straight line from its starting point over time.
• A straight line on a distance-time graph indicates constant speed.
• The slope of the line signifies the magnitude of the speed:
  • Steep slope: high speed.
  • Shallow slope: low speed.
  • Horizontal line: the object is stationary.
• Changing speed is represented by a curve.
  • Increasing slope: acceleration.
  • Decreasing slope: deceleration.
• Speed calculation from a distance-time graph:
  • speed = gradient = {_Delta y} / {_Delta x}

Speed

• Speed is the distance an object travels per unit of time.
• Speed is a scalar quantity (magnitude but no direction).
• Average speed is the total distance traveled divided by the total time taken.
• Formula:
  • average speed = {distance moved} / {time taken}
• Formula triangles can help rearrange equations:
  • Cover the quantity to be calculated.
  • If other quantities are on the same line, they are multiplied.
  • If one quantity is above the other, they are divided.

Core Practical: Investigating Motion

• Objective: To measure the speed of everyday objects.
• Method: Measure distance moved and time taken to calculate average speed.
• Variables:
  • Independent variable: Distance (d).
  • Dependent variable: Time (t).
  • Control variables: Use the same object for each measurement.
• Equipment:
  • Paper cone / tennis ball.
  • Stop watch.
  • Tape measure / metre rule.
• Procedure:
  1. Measure a specific height (e.g., 1.0 m).
  2. Drop the object from this height.
  3. Measure the time taken to fall.
  4. Repeat steps 2-3 multiple times and calculate an average time.
  5. Repeat steps 1-4 for different heights.
• Analysis:
  • Calculate average speed using average speed = {distance moved} / {time taken}.
• Evaluation:
  • Systematic errors: parallax error, human reaction time.
  • Random errors: drafts or breezes.
  • Safety considerations: Use a mat or soft material to cushion the fall.

Acceleration

• Acceleration is the rate of change of velocity.
• Formula:
  • a = {_Delta v} / {t}
  • Where:
    • a = acceleration in meters per second squared (m/s^2).
    • _Delta v = change in velocity in meters per second (m/s).
    • t = time taken in seconds (s).
• Change in velocity:
  • _Delta v = v - u
  • Where:
    • v = final velocity.
    • u = initial velocity.
• An object speeding up has positive acceleration; slowing down has negative acceleration (deceleration).

Velocity-Time Graphs

• Velocity-time graphs display how an object's velocity changes over time.
• A straight line indicates constant acceleration.
• The slope of the line represents the magnitude of the acceleration:
  • Steep slope: large acceleration.
  • Gentle slope: small acceleration.
  • Positive gradient: increasing velocity.
  • Negative gradient: decreasing velocity.
  • Flat line: constant velocity (zero acceleration).
• Acceleration calculation:
  • acceleration = gradient = {_Delta y} / {_Delta x}

Area under a Velocity-Time Graph

• Represents the displacement (or distance traveled).
• Calculate area using:
  • Triangle: Area = 1/2 × Base × Height
  • Rectangle: Area = Base × Height
• Total distance is the sum of all enclosed areas.

Calculating Uniform Acceleration

• Applies to objects moving with constant acceleration.
• Formula:
  • v^2 = u^2 + 2as
  • Where:
    • v = final speed.
    • u = initial speed.
    • a = acceleration.
    • s = distance moved.