Distance-Time and Velocity-Time Graphs: A Compact Presentation of Information
Lesson 9: d-t & v-t Graphs
Graphing the motion of objects gives us a way to interpret the motion that would otherwise be difficult.
● Graphs will also allow you to show a large amount of information in a compact way.
Essentially you need to be able to sketch and interpret two main kinds of graphs in kinematics:
1. Displacement – Time Graphs
● Sometimes called d-t graphs, or position – time graphs.
2. Velocity – Time Graphs
● Sometimes called v-t graphs.
Displacement - Time (d-t) Graphs
This type of graph is based on the most basic things we need to know about the motion of an object
(position and time).
● Typically you will be given a table of values that show the displacement of the object over a particular period of time.
● If the graph shows complex motion (such as Illustration 1 below), you do not just draw a single best fit line. Instead, you need to look at each section of motion and determine what kind of line best fits the data.
● Don't worry too much about sketching these complex situations... it is much more likely that you will draw an object moving in one way only.
● For the example graph shown below, imagine that you are running in a marathon, and we have decided to graph your movement.
Illustration 1: d-t graph of a person running a marathon.
7/22/2011
© studyphysics.ca
Page 1 of 5 / Section 1.2 – 1.4
Now lets look at a description of the person's movement in each of the major sections.
Zero to 90s
Look at how you are running in those first 90 seconds.
● Every 30 seconds you have moved about another
150m away from the starting point… you must be
The slope of a d-t graph always equals moving at a constant positive velocity! the velocity of the object at that time.
● A constant positive velocity is shown on a d-t graph as a straight line that slopes upwards. It is a linear relationship. ● In fact, if you found the slope of the line in this section, it will be the velocity that you were running at. rise d
Graphing the motion of objects gives us a way to interpret the motion that would otherwise be difficult.
● Graphs will also allow you to show a large amount of information in a compact way.
Essentially you need to be able to sketch and interpret two main kinds of graphs in kinematics:
1. Displacement – Time Graphs
● Sometimes called d-t graphs, or position – time graphs.
2. Velocity – Time Graphs
● Sometimes called v-t graphs.
Displacement - Time (d-t) Graphs
This type of graph is based on the most basic things we need to know about the motion of an object
(position and time).
● Typically you will be given a table of values that show the displacement of the object over a particular period of time.
● If the graph shows complex motion (such as Illustration 1 below), you do not just draw a single best fit line. Instead, you need to look at each section of motion and determine what kind of line best fits the data.
● Don't worry too much about sketching these complex situations... it is much more likely that you will draw an object moving in one way only.
● For the example graph shown below, imagine that you are running in a marathon, and we have decided to graph your movement.
Illustration 1: d-t graph of a person running a marathon.
7/22/2011
© studyphysics.ca
Page 1 of 5 / Section 1.2 – 1.4
Now lets look at a description of the person's movement in each of the major sections.
Zero to 90s
Look at how you are running in those first 90 seconds.
● Every 30 seconds you have moved about another
150m away from the starting point… you must be
The slope of a d-t graph always equals moving at a constant positive velocity! the velocity of the object at that time.
● A constant positive velocity is shown on a d-t graph as a straight line that slopes upwards. It is a linear relationship. ● In fact, if you found the slope of the line in this section, it will be the velocity that you were running at. rise d