Solved: The Quadratic Formula from Kinematics In this

Chapter 2, Problem 121

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The Quadratic Formula from Kinematics In this problem we show how the kinematic equations of motion can be used to derive the quadratic formula. First, consider an object with an initial position , an initial velocity , and an acceleration a. To nd the time when this object reaches the position we can use the quadratic formula, or apply the following two-step procedure: (a) Use Equation 212 to show that the velocity of the object when it reaches is given by . (b) Use Equation 27 to show that the time corresponding to the velocity found in part (a) is . (c) To complete our derivation, show that the result of part (b) is the same as applying the quadratic formula to