Position-Time Graphs

Three important notes on position-time graphs:

  • The y-axis represents position.
  • The x-axis represents time.
  • The slope of the graph represents velocity.
    • If the position is in m [N], then a positive slope means the velocity is [N]. If the slope is negative then the velocity is [S].

 

Examples: Day 2, Position-Time Graphs

  1. Peter Parker is on his way to school when he notices the bus is about to leave. He runs to catch it, below is a graph of his movement.
    Peter Catches the Bus

    1. Determine the average velocity of the object in the graph above for the first four seconds.

          \[\begin{align*} \vec{v} &= \frac{rise}{run} \\ &= \frac{8 m}{4 s} \\ &= 2 m/s [N]\end{align*}\]

       

    2. Determine the average velocity of the object in the graph above for the full ten second time interval.
       
      Since the graph is a line, the slope is constant. Therefore, velocity will still be 2 m/s [N].
       
    3. Describe Peter’s motion based on the graph.
       
      Peter runs at a constant velocity of 2 m/s North.
       

     

  2. Later, Spider-Man launches off the top of a building in downtown Manhattan. The graph of his movement is below.
    Peter Jumps Off Building

    1. At what time is Spider-Man travelling the fastest?
       
      At the beginning of his fall, near 0 s.
       
    2. At what time is he travelling the slowest?
       
      At the end of his fall, near 10 s.
       
    3. Estimate his velocity at 10 s.
       
      Spider-Man’s velocity at 10 s is just above 0 m/s [down].
       
    4. Estimate his velocity at 2 s.
       
      Spider-Man’s velocity at 2 s is approximately 1.5 m/s [down].
       
    5. Determine his average velocity between 0 and 10 s.
       
      Determining Spider-Man’s average velocity means drawing a secant of the graph from 0 s to 10 s and then finding the slope of that graph.

          \[\begin{align*} \vec{v}_{avg} &= \frac{rise}{run} \\ &= \frac{10 m}{10 s} \\ &= 1 m/s [down]\end{align*}\]

       

    6. Describe his motion.
       
      Spider-Man falls down off the building, quickly at first but slowing to a stop.
       

     

  3. Consider the following situation:
    • Peter begins by riding his bicycle down the street travelling at 30 m [E] in 4.0 s.
    • He notices police cars zooming down the same street in the other direction, so he stops abruptly for 15 seconds to change into his Spidey costume.
    • He then races West, travelling 60 m in 6.0 seconds.

     

    1. Sketch his motion.
      spider-peter
    2. Determine his overall distance traveled.
       
      Peter travels a total of 90 m.
       
    3. Determine his overall displacement.
       
      His displacement is 30 m [W].
       
    4. Determine his overall time.
       
      Peter travels for a total of 25 s.
       
    5. Determine his average speed.

          \[\begin{align*} v &= \frac{d}{t} \\ &= \frac{90}{25} \\ &= 7.2 m/s\end{align*}\]

       

    6. Determine his average velocity.

          \[\begin{align*} \vec{v} &= \frac{\Delta\vec{d}}{t} \\ &= \frac{30}{25} \\ &= 1.2 m/s [W]\end{align*}\]

       

Practice

Fundamentals of Physics:

  • Pg. 15, #1-4

Related Assignments

  • Assignment E
    • CBR Lab
  • Assignment F
    • Pg. 4, 5 (handout)
  • Assignment G
    • Pg. 8, 9 (handout)
  • Assignment H
    • Pg. 30, # 12
  • Assignment I
    • Pg. 33, #28, 29
  • Assignment J
    • Pg. 35, #43, 44