Position, Velocity, and Acceleration

Basic Concepts

  • Position: The location of an object in space; it is relative and depends on the starting reference; it can be described in different ways, and all descriptions remain valid as long as the reference itself is fixed.

  • Velocity: The rate of change in position with respect to time, and the direction of motion is important.

  • Acceleration: The rate of change in velocity with respect to time.

  • Historical Note: Galileo mathematically described motion, which enabled physics to predict motion mathematically.

Distance and Displacement

  • Distance: The length of the path an object travels to reach the final point, without considering direction.

  • Displacement: The direct difference from the starting point to the end point with direction, i.e., a linear step from start to end.

Choosing the Zero Reference

  • The zero reference should be at a fixed point on the path, preferably simple, and the set of equations depends on it.

  • Example: The library as a zero reference; the school is located at a certain distance from that zero.

  • Values can be positive or negative based on the direction from the reference, and the zero must be kept constant throughout the calculations.

Graphs of Motion

  • PvT (Position versus Time): Displays the object's position over time and provides concentrated information about motion in one place.

  • VT (Velocity versus Time) also exists but the vertical axis differs, and ensure the graph shows position, not velocity, on the vertical axis.

Relationship between Position, Velocity, and Acceleration

  • When position changes quickly, the velocity is:

    • v = \dfrac{\Delta x}{\Delta t}

  • When velocity changes with acceleration, the acceleration is:

    • a = \dfrac{\Delta v}{\Delta t}

PhET Moving Man Experiment

  • Open the PhET The Moving Man simulation and familiarize yourself with the interface: start, sliders, and identify the goal shown in the next slide.

Steps for Drawing and Evaluating PvT

  • Go to the Charts menu in the simulation and select position versus time graph (the blue graph).

  • Use the three available numbers to adjust the graph to be closest to the desired shape.

  • After completion, take a screenshot of the graph with the numbers and submit it.

  • Note for taking a partial screenshot: Cmd + Shift + 3 or Cmd + Shift + 4 (for Mac).

Quick Review Points

  • Position is relative and depends on a fixed reference.

  • The fundamental difference between distance and displacement.

  • Basic relationships: v and a as in the equations above.

  • The difference between PvT and VT in graphical representation.

  • The importance of PvT in analyzing an object's motion over time.