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This module is part of a collection of modules that were developed to support laboratory activities in a Precalculus for PreEngineers (MATH 1508) at the University of Texas at El Paso. Contained in this module of applications of quadratic equations in various fields of engineering and science. These include the motion of an object under constant acceleration, quantitative management, and break-even analysis.

Quadratic equations


Quadratic equations play an important role in the modeling of many physical situations. Finding the roots of quadratic equations is a necessary skill. Being able to interpret these roots is an important ability that is important in understanding physical problems. In this module, we will present a number of applications of quadratic equations in several fields of engineering.

Determining the roots of quadratic equations

A quadratic equation has the following form

ax 2 + bx + c = 0 size 12{ ital "ax" rSup { size 8{2} } + ital "bx"+c=0} {}

Because a quadratic equation involves a polynomial of order 2, it will have two roots. In general, a quadratic equation will either have two roots that are both real or have two roots that are both complex. For the present module, we will restrict our attention to quadratic equations that have two real roots.

There are three methods that are effective in solving for the roots of a quadratic equation. They are:

  • Solution by factoring
  • Solution by completing the square
  • Solution by the quadratic formula

The applications that follow will include examples of each of these three methods of solution.

Motion of an object under uniform acceleration

We will begin our study of quadratic equations by considering an application that you will likely encounter later in physics and mechanical engineering classes. Let us consider an object that is subject to a uniform acceleration. By uniform, we mean an acceleration that is constant. Such an object might be an automobile, an aircraft, a rocket, etc. The motion of an object subjected to uniform acceleration can be expressed mathematically by the following equation.

s ( t ) = 1 2 a t 2 + v 0 t + s 0 size 12{s \( t \) = { {1} over {2} } `a`t rSup { size 8{2} } +v rSub { size 8{0} } t+s rSub { size 8{0} } } {}

where s ( t ) represents the position of the object as function of time t ,

a represents the constant acceleration of the object,

v 0 represents the value of the object’s velocity at time t = 0, and

s 0 represents the position of the object at time t = 0.

An equation of this sort is called an equation of motion . We will illustrate its use in the following exercise.

Example 1: For our first example, let us consider a dragster on a drag strip of length one-quarter mile. For time t<0, the dragster is at rest at the starting line. At time = 0, the driver depresses his gas pedal to produce a uniform acceleration of 50 m/s 2 . Under these conditions, how far will the dragster travel in 1 second?

Because the dragster travels in a horizontal direction, we will represent its distance from the starting point as a fuction of time as x ( t ). We also know that the value for the acceleration ( a ) is 30 m / s 2 . We can incorporate these changes in equation (1) to produce a new equation of motion for the dragster.

Questions & Answers

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s. Reply
how to fabricate graphene ink ?
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What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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I'm interested in nanotube
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Ramkumar Reply
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Sravani Reply
what is system testing?
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Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
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I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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Smarajit Reply
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Can someone give me problems that involes radical expressions like area,volume or motion of pendulum with solution

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Source:  OpenStax, Math 1508 (laboratory) engineering applications of precalculus. OpenStax CNX. Aug 24, 2011 Download for free at http://cnx.org/content/col11337/1.3
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