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.
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
● In fact, if you found the slope of the line in this section, it will be the velocity that you were running at.
90s to 150s
Yikes! You ran too fast at the start and now you’re out of breath!
● During this time period, your position on the graph
has stayed the same…450m.
● This just means that you are standing in the same
spot, exactly 450m away from where you started.
● A flat horizontal line means you are stopped.
The slope of the line is the velocity, and
the slope of a flat line is zero. So, the
velocity is zero.
150s to 240s
You must have started running forward again, since a positively sloped line means a positive velocity. ● Notice that this section of line is a little steeper than the first section. You are now running about 200m every 30s.
● A steeper line (which has a bigger slope) means that you are moving at a faster constant velocity.
240s to 300s
In this section the line slopes down, which means it has a negative slope. ● Since slope is equal to velocity, this must mean that you are running backwards. ● A negative slope means a constant negative velocity.
● You must have forgotten to pass a check point, so you ran back to it.
300s to 360s
Again, we have a horizontal line. You must be stopped.
360s to 510s
You know that you have only one chance to still win the race… run as fast as you can! ● During this time period, the line curves upwards.
● The line becomes steeper and steeper as it continues. This means that the slope of the line is getting bigger and bigger.
Page 2 of 5 / Section 1.2 – 1.4
Since slope is related to velocity, your velocity must be increasing. You are accelerating!
A curved line on a d-t graph means
A curved line on a d-t graph means
acceleration is happening.
Here’s how you can remember if it was positive or negative acceleration on a d-t graph.
Illustration 2: Happy
Illustration 3: Unhappy
If you see any part of the happy clown's face on a graph, it is positive acceleration. If you...
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