SOLUTION: Hello tutor,, I don't understand this math word problem and I was wondering if you could help me solve it. It is suppose to be solves by using quadratic inequalities in one variabl

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Question 1094357: Hello tutor,, I don't understand this math word problem and I was wondering if you could help me solve it. It is suppose to be solves by using quadratic inequalities in one variable.
The kinetic energy of a moving object is related to its mass and velocity by the formula.
Ek=1/2mv^2, where Ek is the kinetic energy in joules (J), m is the mass of the object in kilograms, and v is the objects velocity in meter per second. what are the possible velocities for a 3kg object with a kinetic energy of less than 600J?(negative velocities are acceptable and represent the opposite direction of a positive velocity.)
thank you so much for your help:)
Answer by ikleyn(52750) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  It is easy.


2.  Everything is just given to you to write this basic inequality for kinetic energy

        Ek < 600,


    which is the same as 

        %28m%2Av%5E2%29%2F2++ < 600,

    or

        %283%2Av%5E2%29%2F2 < 600.


    It gives you 

        v%5E2 < %28600%2A2%29%2F3 = 400,

    and, after taking the square root from both sides,

        -20 < v < 20.


Answer.  In order for kinetic energy was less than 600 Joules, the speed of the given body must be  in the range from -20 m/s to 20 m/s.