For choosing an
appropriate gap between your car and the car in front. How do these models
compare with each other?
The distance model recommends gaps between vehicles at
various speeds, so you can compare this model to time model by calculating the
gaps between vehicles at the same speed when the two second rule is observed. So
we need to calculate these gaps.
Gaps for the time
model
you can calculate the gap between cars given by the two second
rule by substituting the time of two second and the relevant speed into the
formula “distance= speed × time”. To make a comparison with the distance model
possible, we want the answer to be in metres. Therefore, this speed used in the
far more must be expressed in m/s. However, this speed is that we need to
consider- those in figure said are expressed in mph and km/h.
Example 5 converting km/h into m/s
convert 32km/h to m/s. Give your
answers to 3 significant figures.
Solution
the speed of 32km/h means that
in 1 hour the card travels 32km, that is,
32× 1000 = 32 000m.
Since there are 60 minutes in an
hour the 60 seconds in each minute, there are 60×60= 3600 seconds in an
hour.
So the card travel is 32 000m in 3600 seconds.
Therefore in one second, the car travels
m = 8.888m.
m = 8.888m.
So 32km/h is 8.89m/s (to 3S.F.).
Drawing
a graph
Although it is possible to compare the
results by looking at the data in the table in the solution, a graph can be
helpful. This has the advantage of illustrating overall features, which may not
be so clear from the numerical data.
Tips for drawing a graph or chart based on data
Ø
include a clear title and the source of the data.
Ø
Label the axes when then names of the quantities and the units.
Ø
Mark the scale is clearly, choosing the scale that are easy to
interpret and that make good use of the space available.
This is a graph of speed measured in
m/s plotted against speed measured in km/h, based on the data given for this
conversion in the table in activity 10. This kind of graph is known as a conversion
graph because you can use it to convert from one unit to another.
The graph has been drawn by choosing the
horizontal axis to represent this speed in km/h and the vertical axis to
represent this speed in m/s. These scales have been chosen so that it is easy
to plot points and leadoff values. If all the values on the vertical axis are
between 52 and 70, then the points are more spaced out and clear if part of the
vertical axis is omitted. The axis scale does not start at 0, then they should
be indicated either by drawing to angled parallel lines. The points
representing the pair of values (32, 8.89) have been plotted opposite 32 on the
horizontal axis and opposite 8.89 on the vertical axis. The horizontal
coordinate and represents the distance the point is to the rate of 0 on the
horizontal axis. The 2nd value in the pair, 8.89, is known as the
vertical coordinate and represents the distance the point is above 0 on the vertical
axis.
You can use it either dots, or small
crosses to mark the point on a graph. Crosses are often easier to use,
particularly beforehand wrong graphs, as they mark points precisely and are
clearly visible.
Interpreting the graph
you
can use the graph on the previous page to convert speed measured in km/h to m/s
and vice versa, as illustrated in the next example.
Example 6 converting
speeds
use the graph in figure 7 to make the following conversations.
(A)
convert 75km/h tom/s
(B)
convert 5m/s to km/h
Solution
(A)
find 75 on the “speed (km/h)” axis, rather line particularly up
to the graph and then draw another line horizontally across to “speed (m/s)”
axis, as shown by the short red dashes on the graph in figure 9. Read the
number on the vertical axis. A speed of 75km/h is approximately 21m/s.
(B)
Find 5 on the “speed (m/s)” axis, draw a line horizontally
across to the graph and then draw another line particularly down to the “speed
(km/h)” axis, as shown by the long blue dashes on the graph in figure 9. Read
of the number on the horizontal axis. A speed of 5m/s is approximately 18km/h.
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