Time-Distance Graphs and Motion Concepts Summary

Motion Vocabulary

  • Speed:

    • Definition: The distance traveled per unit of time.
    • Formula: extSpeed=extDistanceextTimeext{Speed} = \frac{ ext{Distance}}{ ext{Time}}
    • Example: If a car travels 100 meters in 5 seconds, its speed is 100extm5exts=20extm/s\frac{100 ext{ m}}{5 ext{ s}} = 20 ext{ m/s}.

  • Velocity:

    • Definition: The speed of an object in a given direction.
    • Example: If a skateboarder moves east at 5 m/s, their velocity is 5 m/s east.

  • Acceleration:

    • Definition: The rate of change of velocity.
    • Formula: a=extChangeinVelocityextTimea = \frac{ ext{Change in Velocity}}{ ext{Time}}
    • Example: If a car speeds up from 20 m/s to 40 m/s in 2 seconds, ( a = \frac{40 ext{ m/s} - 20 ext{ m/s}}{2 ext{ s}} = 10 ext{ m/s}^2 $$.

Distance-Time Graphs

Key Concepts
  • Graph Representation: The slope of a distance-time graph indicates the speed. A steeper slope equals a higher speed.
  • Flat Line: Represents no movement (speed = 0).
  • Straight, Sloped Line: Indicates constant speed.
  • Curved Line: Represents changing speed (acceleration).

Motion Scenario Analysis

Scenario 1: Skateboarder
  • Description: Rides through the park at a constant speed of 5 m/s.
  • Graph Representation: A straight line with a slope representing 5 m/s.
  • Explanation: The line is straight because the speed is constant.
Scenario 2: Vehicle Movement
  • Description: A vehicle moves 10 meters in 1 second, stays motionless for 1 second, then moves 10 meters in 2 seconds.
  • Graph Representation:
    • Part 1: A straight line with a steep slope for the first second (10 m in 1 s).
    • Part 2: A flat line for 1 second (motionless).
    • Part 3: A less steep line for the next 2 seconds (10 m in 2 s).
  • Explanation: The changing slopes represent different speeds; the flat line denotes the stationary phase.
Scenario 3: Jet Aircraft
  • Description: Takes off from a runway and climbs to 500 meters.
  • Graph Representation: A steep upward line that quickly reaches the height (500 m).
  • Explanation: The steep slope indicates rapid ascent (high speed).
Scenario 4: Vehicle Coasting
  • Description: A vehicle travels at constant speed and then coasts to a stop for 10 seconds.
  • Graph Representation: A straight line that decreases in slope as it approaches 0 m (coasting). Ends with a flat line for the 10 seconds.
  • Explanation: The gradual decrease indicates deceleration until it stops. The final flat segment indicates it remains stationary for 10 seconds.