Basic Background Information about Relationship of Time vs. Distance at a
Constant Speed
What shape do we get when graphing distance vs. time at a constant speed?
The motion of objects can be represented using graphs to show the relationship between two factors. In this
case, distance and time. Using graphs students are able to get a wonderful visual of the type of slope
associated with the data. The students will easily grasp the relationship between time and distance by
graphing their data.
Constant Speed (2 mph)
Time (hrs) Distance (mi)
1
2
2
2 +2= 4
3
4 +2= 6
4
6 +2= 8
5
8 +2= 10
6
10 +2= 12
7
12 +2= 14
8
14 +2= 16
9
16 +2= 18
10
18 +2= 20
Let’s begin! The family is moving throughout the park at a constant speed. This is
important to allow student to understand motion at its basic level and then build
upon their prior knowledge. So going back to the start, the family is traveling
throughout the park at a constant speed of 2 mph they are traveling really slowly!
So let’s break that down, that would mean that the family is walking 2 miles per
hour. If we create a chart for this constant speed it would look like this. (See data
table to the right)
If we graph this data, it would look like the graph below a straight line increasing at
a constant positive speed upward towards the right.
Constant Speed
Now if we have changing
speed, that is family is
speeding up or
accelerating. We get a
different set of data.
Our data might look
something like the data
table on the right.
Distance (miles)
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
Changing Speed (1-6 mph)
Time (hrs) Distance (mi)
1
1
2
1+2=3
3
3 +3= 6
4
6 +3= 9
5
9 +4= 13
6
13 +4= 17
7
17 +5= 22
8
22 +5= 27
9
27 +6= 33
10
33 +6= 39
If we graph this data it
would like the graph
shown below. Notice
the straight line has
changed to a curved
slope.
Time (hr)
Changing Speed (1-6 mph)
This concept informs us of a very important principle. The
principle that the slope of the line on a time vs. distance
graph tells us about the motion of the object. There is a
saying, “As slope goes, so goes the speed.” So if speed is
increasing, so too will the slope of the line (ex. curved
line). If speed is constant, the slope is constant. (ex.
straight line) This principle can be applied to any motion
possible.
It is important to note that depending on speed (how fast
or slow) object is traveling; the slope of the line varies. If
we apply velocity to this principle, change in direction,
the slope of the line will also vary greatly. You can go to
the following website for help with this concept.
http://www.physicsclassroom.com/class/1dkin/u1l3a.cfm
Distance (mi)
The importance of Slope!!!!
45
40
35
30
25
20
15
10
5
0
1
2
3
4
5
6
7
Time (hrs)
8
9 10