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Mathproject 1

1) The document analyzes the speed of a 2010 Corvette racing down a quarter mile drag strip. Data on the car's distance over time is fitted to a 4th order polynomial function. 2) By taking the derivative of the position function, a velocity function is derived. Setting this equal to 60 mph and solving gives a time of 4.0933 seconds for the Corvette to reach 60 mph. 3) Error analysis shows the error in the distance equation decreases with increasing time and distance, staying below 14% for early data points.

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48 views2 pages

Mathproject 1

1) The document analyzes the speed of a 2010 Corvette racing down a quarter mile drag strip. Data on the car's distance over time is fitted to a 4th order polynomial function. 2) By taking the derivative of the position function, a velocity function is derived. Setting this equal to 60 mph and solving gives a time of 4.0933 seconds for the Corvette to reach 60 mph. 3) Error analysis shows the error in the distance equation decreases with increasing time and distance, staying below 14% for early data points.

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api-346180350
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Name:

Robert Souders,

Math 151.02
Project: Speeding Car
Foreword
This is a mathematical analysis of a 2010 Corvette racing a quarter mile concrete drag
strip. The data given gives distances traveled in feet relative to time in seconds. The data was
put into a stat plot and used to derive a power equation to the 4th power. The derivative
equation was derived from the original function and the time for the Corvette to reach 60mph
was calculated.

Analysis:
How long does it take for the corvette in seconds to reach 60 mph?

Distance Time in seconds converted to hours

1 foot = 0.000189 mile 0.734 sec = 0.000205 hours

60 feet = 0.011364 mile 2.063 sec = 0.000573 hours

330 feet = 0.0625 mile 5.387 sec = 0.001496 hours

mile = 0.125 mile 8.025 sec = 0.002229 hours

1000 feet = 0.189394 mile 10.312 sec = 0.002864 hours

mile =0.25 mile 12.259 sec = 0.003405 hours


1. Data of the Corvettes distance relative to time down a quarter mile track.

The power function to the 4th power of the data table was calculated using a TI-86 and the
polynomial regression analysis.

f(t)= -0.006344 t4 -0.057759 t3 +9.03156 t2 +18.7086t-17.2155


This equation is for the position of the corvette.

The velocity is the derivative of f(t) position function.

f (t)= (4)(-0.006344) t3 +(3)(-0.057759) t2 +(2)(9.03156)t+18.7086 ft/s


V(t)= -0.025376 t3 -0.173277 t2 +18.06312t+18.7086 ft/s

To find the time, first convert our velocity equation to mi/hr by multiplying by the conversion.
3600sec 1mi
1hr 5280ft = 0.681818 (sec mi)/(hr ft)
V(t)= (-0.025376 t3 -0.173277 t2 +18.06312t+18.7086)(.68181818) mi/hr
V(t)= -0.017302 t3 -.118143 t2 +12.31576t+12.755911 mi/hr

Now we set V(t)=60 and solve for t to find the time in seconds that the car reaches 60 mi/hr.

60 mi/hr = -0.017302 t3 -.118143 t2 +12.31576t+12.755911


Was solved using TI-86 in the solver program

t= 4.0933 sec
We can conclude that t=4.0933 is the correct answer of the three because of the graph linked
below. The corvette will reach 60mph at about 4.0933 seconds.
https://www.desmos.com/calculator/favb40lfqs

Error:
The error for the distance equation becomes less significant as the time and distance increases.
The numbers below is data taken from the chart 1 and the distance equation. The velocity
equation should have a small error in correlation with the distance equation. This error percent
may also be varied depending on the error from the original source the distance and time data
was taken from.

Distance Time in seconds Distance Equation %Error

1 foot = 0.000189 mile 0.734 sec 1.1357 ft 13.57%

60 feet = 0.011364 mile 2.063 sec 59.196 ft 1.34%

330 feet = 0.0625 mile 5.387 sec 31.289 ft .3906%

mile = 0.125 mile 8.025 sec 658.40 ft .2429%

1000 feet = 0.189394 mile 10.312 sec 1001.0 ft .1028%

mile =0.25 mile 12.259 sec 1319.7 ft .0205%


2. Percent error of data given compared to derived distance equation.

Conclusion:
After running a mathematical analysis using the TI-86 and then taking the derivative of the
equation calculated to find the velocity equation, we then graphed this velocity equation in
Desmos and have determined that the Corvette will accelerate to the velocity of 60mi/hr in
approximately 4.0933 seconds.

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