2020 - Day 9 - Velocity-Time Graphs & Displacement - Presentation

Velocity-Time Graphs and Displacement

  • A velocity-time graph indicates the velocity of a moving object over various times.

  • The slope of a velocity-time graph represents the object's acceleration.

  • The area under the velocity-time graph represents displacement.

Sample Problems

  • Problem 1: Displacement of a car over a 10 s interval.

    • Formula Solution:

      • Displacement (d) = Average Velocity (V) × Time (t).

      • d = V × t → d = 20 m/s × 10 s = 200 m.

    • Graphing Solution:

      • Area (A) = Base × Height.

Graphing Examples

Problem 2

  • Ball Rolling Downhill:

    • Graphing Solution:

      • Displacement (d) after 10 s = Area under graph.

      • A = 1/2 × Width × Height → Area = 1/2 × 10 s × 20 m/s = 100 m.

Problem 3

  • Dog Running Along Road (16 s Interval):

    • Long Graphing Solution:

      • Total Displacement (d) calculated as:

      • Sections calculated separately and then added.

      • Include integration of area under curve for various speed segments.

Introduction to Area Calculation

Definition of a Trapezoid

  • A trapezoid is defined as a quadrilateral with at least one pair of parallel sides.

  • Area Formula:

    • Area = 1/2 × (Base1 + Base2) × Height.

Calculating Displacement with Trapezoidal Areas

Problem 4

  • Car Motion Analysis:

    • Total displacement achieved via trapezoidal area calculation method using speed over time.

Problem 5

  • Child Playing:

    • Displacement determined by calculating areas of various segments under the graph.

Analysis Techniques

Area Under the Velocity-Time Graph

  • The algebraic sum of the areas under the velocity-time graph yields the overall displacement.

  • Positive areas above the time axis represent forward movement, while negative areas below indicate a backward movement.

Advanced Velocity-Time Graph Problems

Mouse Movement Analysis

  • Velocity vs. Time Graph:

    • (a) Calculate displacement over initial 3 seconds.

    • (b) Calculate displacement between 4-6 seconds.

    • (c) Determine total displacement.

    • Average speed and average velocity formulas applied over intervals.

Motorcycle Motion Analysis

  • (a) Maximum displacement west.

  • (b) Resultant final displacement.

  • (c) Total distance traveled over 70 seconds.

  • Calculate average speed and velocity using formulas based on graph areas.

Practice Problems

Average Speed and Velocity Analysis

  • Problems assessing speed between various time intervals using graph data.

  • Questions about average velocities during specified intervals, computing the average based on the areas and times specified.

Overall Displacement during a Trip

General Queries

  • Determine displacement during specific intervals, resulting in calculations for resultant displacement and average velocity.