<::Distance-Time Graphs::>

Distance-Time
Graphs

:: | Distance - Time | ::


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Distance-time graphs is a way to visually show a collection of data. It allows us to undertstand the relationships between the data.

The below is a example of a distancetime graph, the time

Distance-Time for Table 1

Distance(m)
Time (s)

Distance (s)	Time (s)
0	0
1	13
2	25
3	40
4	51
5	66
6	78

As you can see, the data from the table is shown in a visual format in the graph. The time(s) is shown as the x axis and the distance(m) is shown on the y axis on the graph. The points on the graph do not create a perfectly straight line so a line of best fit must be drawn in.

The proper equation for a line is y=mx + b
The y is the dependant variable (on y -axis)
The x is the independent variable (on x-axis)
The m is the slope of the line
The b is the y intercept of the line.

In a distance-time graph the equation changes from
y= mx + b
To
d = vt

d is the dependant variable, lying on the y axis.
t (time) is the independant variable and lies on the x axis.
v (speed) is the slope of the line.
0 (the initial distance) is the y intercept.

Slope and the Speed

When you look at a slope of a line on a distance-time graph you may notice how slopes can be different. The slope of the line determines the speed; the higher the slope the greater the speed, but if the slope is low then the speed is low. Lets looks at the examples below

As you can see in the first chart, the slope is very high, this means that the car must be traveling at a great speed. In the second graph, the slope is relatively low, which means that the car is driving at a very low speed

As you might recall from math class, the slope of a line is equal to the rise(y) divided by the run (x). To translate this to d to fit in with a distance-time and time graph, the slope(speed) is equal to the change in distance(d) divided by the change in time(t). The speed is determined from the line of best fit on a distance-time graph.

slope = rise/run
or
v= d / t

The slope of the line is calculated as followed

d = d₂ -d_{1

d =
7.7km - 1.9}km
d = 5.8km

t = t₂ - t_{1

t =
11.2min - 2.7min

t = 8.5min}

v = d/t
v = 5.8/8.5
v=0.68km/min

*remember significant digits digits rule still applies
**Note the speed of a object in motion can be determined the slope of a distance -time graph.

Continue to the next lesson: ::Acceleration::