Distance, Velocity time graph
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Distance-time Graph

  1. What is a distance-time graph?
         A distance-time graph simply shows the relationship between time and position.
    For example, given the following data,  plot the position-time graph? We can draw the following graphs.
    Data

    time (s)

    		 position (s)
    0 0
    1 20
    2 50
    3 130
    4 150
    5 200
  2. How do we evaluate the average velocity between two points? 
         The tangent of a distance-time graph represents velocity since
  3. From the given curve,  what is the average velocity during the first 2 seconds?
  4. From the given curve,  what is the average velocity of the whole trip?
  5. Using the following distance-time graph describe the motion.
    No Segment Description  Distance Velocity  Acceleration
     1  Linear, +slope increasing constant zero
    2 Curved-up increasing increasing increasing
    3 curved-down increasing decreasing decreasing
    4 straight-line constant zero zero
    5 curved-down decreasing increasing increasing
    6 curved-up decreasing increasing increasing
    7 linear, -slope decreasing constant zero
    8 linear, -slope increasing constant zero
    9 curved-down increasing not constant increasing
    10 curved-up increasing decreasing decreasing
    11 straight-line constant zero zero
    12 curved-down decreasing increasing increasing
    13 curved-up decreasing increasing increasing
    14 linear, +slope decreasing constant zero
 

Velocity-time Graph

  1. What is velocity-time graph?
    A velocity-time graph shows the relationship between velocity and time. 
  2. If a car moves at constant velocity of 5 m/s for 10 seconds. Plot a velocity-time graph. 
    Data

    time (s)

    		 Velocity (s)
    0 20
    1 21
    2 24
    3 27
    4 28
    5 30

     
  3. What are the types of data that we can obtain from a velocity-time graph?
         1- Instantaneous velocity at any time
         Directly from velocity axis
    2- Average Acceleration at any time interval (ti,tf)
         a=Vf-Vi/(tf-ti)
    3- Traveled Distance at any time interval (ti,tf)
         Traveled Distance=Area Under the curve between ti and tf.
         The area below the line represents the displacement the object traveled since it can
         be calculated by (time * velocity) which equals to displacement.
    4- Average-velocity at any time interval (ti,tf)
         Average-velocity=Traveled Distance/(tf-ti)
  4. What is the significance of the area under the velocity-time curve 
          The area below the line represents the displacement the object traveled since it can
         be calculated by (time * velocity) which equals to displacement.
  5. What is the significance of tangent of a velocity-time graph?
     the tangent of a velocity-time graph represents instantaneous acceleration since
     For example, the instantaneous acceleration when t = 3 at the below graph is 3 m/s2, since the graph has a slope of 3 when t = 3.
  6. What is the instantaneous acceleration of the above object when t = 0?
  7. What is the average acceleration of the whole trip? (When t = 7, velocity = 26 m/s)
  8. Does above object has a constant acceleration?
  9. Using the following distance-time graph describe the motion.


    1. No path Segment Description  Velocity  Acceleration
       1  AB Linear, +slope increasing constant
      2 BC Curved-down increasing decreasing
      3 CD straight constant zero
      4 DE Linear, - slope decreasing constant deceleration
      5 EF straight stationary zero
      6 FG Linear, - slope decreasing constant
      7 GH straight constant zero
      8 HI linear, +slope increasing decreasing
       

      Distance=A1+A2
      Displacment=A1-A2
  10. Using the following distance-time graph describe the motion.
    No Segment Description  Velocity  Acceleration
     1  Linear, +slope increasing constant
    2 Curved-up increasing increasing
    3 curved-down increasing decreasing
    4 straight-line constant zero
    5 curved-down decreasing decreasing
    6 curved-up decreasing decreasing
    7 linear, -slope decreasing constant
    8 linear, -slope increasing increasing
    9 curved-down increasing increasing
    10 curved-up increasing increasing
    11 straight-line constant zero
    12 curved-up  increasing increasing
    13 curved-down  increasing increasing
    14 linear, +slope  constant constant
     

    Distance=A1+A2
    Displacment=A1-A2

    		    

For more information write: abumsamh@emirates.net.ae
Created SEP 1, 2000
Copyright © 2000
Designed by: R. K. Abu-Msameh
Last modified: October 06, 2000