Morgan Godley
5/2/11
MAT 266
Honors Contract
Is Speeding Worth the Risks?
Today, it speeding is normal. There is a set speed limit for every street, but
really drivers do not consider the speed limit on the sign the speed limit. Most
people define the “speed limit” as the highest speed they can drive without getting a
ticket. For instance, in Arizona, the “speed limits” turn into 7 over on surface streets
and 10 over on the high way. This is how the flow of traffic drives, and there are
daredevils that speed even faster than this.
But the fact is, speeding leads to problems. It is harder to drive defensively at
high speeds and then also when a speeder crashes, the impact is more dangerous
than one at lower speeds. Speeding is a factor in one third of all lethal accidents. In
1998, speeding killed about 42,000 people and injured a 3.2 million people. On a
fiscal note, the United States pays about $27.7 billion dollars yearly because of these
crashes, which comes to about $144 per taxpayer. Knowing this, the question comes
to mind: is speeding worth the risks? A dedicated speeder would be hard to
persuade: most speeders are convinced they are great drivers while speeding and
they speed because they save sufficient time.
The only way speeding could make an effective argument is if it saves
substantial time. The question is: how much time does speeding save a given driver?
Using calculus to calculate velocities, accelerations and positions from section 9.2 in
Essential Calculus and some traffic law values, this project calculated how much time
speeders can save or waste on surface streets. Lights are timed so that the light
should turn green the second the driver arrives at the stoplight and decelerates to
0ft/s, if he or she is going the speed limit. Ideally, all the time a speeder saves is time
wasted waiting at a stoplight.
Most surface streets have 35 miles per hour speed limit, which is equivalent
to 51.3 ft/s. A typical “slow” driver would probably accelerate to this speed in 15
seconds. This given, the acceleration comes to +3.42ft/s2, assuming constant
acceleration. While accelerating, the driver travels 171.1 feet. Since the driver
ideally then decelerates to 0ft/s once he or she arrives to the stoplight, the driver
will then also travel 171.1 feet as he or she decelerates at the end of the journey. The
average stoplights are 2800 ft apart, from beginning of the drive to the end. Since
the driver travels 342.2 ft while accelerating and decelerating, that means the driver
travels 2457.8 ft at the speed of 35 miles per hour. It takes the driver 47.9 seconds
to drive this far at the speed limit. Now that all three parts have been solved for,
acceleration, cruising, and deceleration, the total time for the law-abiding driver
comes to 77.88 seconds.
Visually, the trip is like this:
The calculations for these values are as follows:
v=35mi/hour=35mi/hour * 5280ft/mi * hr/3600s = 51.33 ft/s
v=v0+at
where v0=0ft/s because the driver is beginning from rest
a=v/t=(51.33ft/s)/15s=3.42ft/s2
x=

15
 adt 
0


15
15
0
0
 3.422dt 
 (3.422t  c)dt
where c=v0=0ft/s
=((1/2)3.422t2+c)|150
where c=x0=0ft
x=171.1ft
x35mph=2800-(171.1*2)=2457.8ft
x=∫vdt=vt  t=x/v
t=x35mph/v=2457.8/51.33ft/s=47.88s
∑t=taccel+t35mph+tdecel=15s+47.88s+15s=77.88s
It is then appropriate to calculate all of these values for a speeder. For
instance, take the average speeder who is going 10 mph over the speed limit, going
45 mph, or equivalently 66ft/s. Given that he or she has more of a lead foot, it
probably takes about 10 seconds to accelerate. Given a constant acceleration, the
acceleration comes to 6.6 ft/s2 and the driver travels 330 ft in this time. Given that
the driver both accelerates and decelerates to and from 0ft/s, that leaves 2140ft to
travel at 45mph. He or she travels this distance in 32.42 seconds. The total time it
takes the 45mph speeder to travel from stoplight to stoplight is 52.42 seconds.
Visually, this is the 45mph driver’s trip:
The calculations for these values are as follows:
v=45mi/hr * 5280ft/mi * hr/3600s = 66ft/s
a=v/t=(66m/s)/10s=6.6ft/s2
x=

10
10
10
0
0
0
  adt    6.6dt   (6.6t  c)dt
where c=v0=0ft/s
=((1/2)6.6t2+c)|100 where c=x0=0ft
x=330ft
x45mph=2800ft-(330ft*2)=2140ft
x=∫vdt=vt  t=x/v
t=2140ft/(66ft/s)=32.42s
∑t=taccel+t45mph+tdecel=10s+32.42s+10s=52.42s
A driver going 15mph over the speed limit, 50mph or 73.33ft/s, takes even a
little less time. If this driver accelerates to 50mph in 8 seconds, given constant
acceleration, he or she accelerates at 9.167ft/s2 and in that time travels 293.3ft.
Since the driver needs to both accelerate and decelerate, that leaves 2213.3ft to
travel going 50mph. He or she travels this distance in 30.18 seconds. Knowing all of
these times, the total time from one stoplight to the next comes to be 46.18 seconds.
The calculations for these values are as follows:
v=50mi/hr * 5280ft/mi * hr/3600s =73.33ft/s
a=v/t=(73.33ft/s)/8s=9.1667ft/s2
x=

8
8
8
0
0
0
  adt    9.1667dt   (9.1667t  c)dt
where c=v0=0ft/s
=((1/2)9.1667t2+c)|80
where c=x0=0ft
x=293.3ft
x50mph=2800ft-2*293.3ft=2213.3ft
x=∫vdt=vt  t=x/v
t=2213.3ft/(73.33ft/s)=30.18s
∑t=taccel+t35mph+tdecel=8s+30.18s+8s=46.18s
Now that all of these values have been found, the benefits from speeding can
be found. The lights are time so that once the drivers going the speed limit hit the
intersection, decelerated to 0ft/s, they should turn green.
The time differences for one stoplight are as follows:
v (mph)
35
45
∆t (s)
0
25.46
50
31.7
These were calculated by subtracting the speeders’ times from the 35mph’s.
Fig-1
Ideally, there is no time wasted for the law-abiding driver sitting at
stoplights. This means that whatever the speeder beats the law-abider by the
speeder should be sitting impatiently at the stoplight for that amount of time.
The time differences for different distances are as follows:
v (mph)
35
45
∆t for 1.89 mi (min)
0
0.424
∆t for 5.67 mi (min)
0
1.27
∆t for 9.45 mi (min)
0
2.12
∆t for 15.12 mi (min) 0
3.39
∆t for 20.79 mi (min) 0
4.67
50
0.528
1.59
2.64
4.22
5.81
Fig-2
All of these distances are exact distances with the stoplights: 1, 3, 5, 8 and 11.
The differences of time in seconds was multiplied by the number or intersections, to
get the difference in seconds over that distance, and then divided by 60s to get the
difference in minutes.
Ideally, because of timed lights, the differences in time in Figure Two are the
times that the speeders wait idly at the stoplights, waiting for the light to change.
However, in real life, traffic backs up. By speeding, the speeder may be able to push
his or her way to the end of the back up and catch that light, thus saving time. If the
speeder is lucky enough to catch this back up every time, he or she, instead of
wastes that difference in time, gains that difference, and arrives at location that
much sooner. Therefore, only if the speeder is extremely lucky, they will get that
maximum time saved.
By examining Figure Two, speeding does not have great benefits. Even over
at 20.8 mi journey, which is far longer than the average driver, the 45mph driver
could save 4.67 minutes and the 50mph driver 5.81 minutes, if they both catch all of
the backed up lights. Five to six minutes is not that much time: no one is going to be
too upset if their guest or employee arrives five to six minutes late. Similarly, it is
not that difficult to leave the house five to six minutes earlier. But on average
speeding does not even save that much time. An average distance for most cars is
from 5 to 15 miles. The 45mph driver would save 1.27 to 3.39 minutes and the
50mph driver would save 1.59 to 4.22 minutes, again if they both were lucky
enough to catch all of the lights. Again, this is not substantial time.
This report assumes that all the speeds and accelerations are constant. While
actually driving, most speeders will have slow drivers in their paths, making them
not accelerate as quickly as they like and not maintain their high speeds. This makes
them save even less time. Conversely, there could be areas where the speeders can
speed even higher than 10 or 15 over, allowing them to save even more time.
However, given the calculated results in Figure Two, going even just a little bit faster
really is not going to gain any substantial time.
By looking at these values that speeding could save in Figure Two, many can
come to the conclusion that speeding is not worth the risks. The time it could save is
not very much. No one will care if a driver is five minutes late to an event, especially
if they are thinking of his or her safety. Similarly, it is not difficult to leave five
minutes earlier than normal, making speeding not a necessity. The benefit of
speeding, getting there faster, really is not a substantial benefit in any regard.
Furthermore, weighing the benefit of saving time against the high likeliness of
crashing, potentially a lethal crash, is all the more convincing to not speed.
Today the majority of people speed. However, upon looking at the results in
Figure Two, speeding does not save that much time because of timed lights. When
the benefit of saving a small amount of time is weighed against the fact that
speeding causes one third of all accidents, many can conclude that there is no
benefit to speeding.
Works Cited
“Traffic Signals.” The Electric Department of the City of Oak Ridge, 2010. Web. 28
Apr. 2011
United States. Advocates for Highway & Auto Safety. “Fact Sheet: Speeding”
Washington DC: 2005. Web. 28 Apr. 2011.
United States. Governors Highway Safety Association. “Speeding” Washington DC:
2011. Web. 28 Apr. 2011.