Is The Equation Vf = Vi + Ax Dimensionally Correct?

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The answer depends somewhat on whether this is being presented as an algebraic equation, where "x" is a variable to be solved for, or if the equation is a formula for calculating a final velocity Vf given the initial velocity VI, an Acceleration A and a distance x.  If that is the case, the formula is not dimensionally correct and thus the formula itself can not be correct.  To see this, suppose the unit of distance is feet and  time is in seconds,  being velocities, both VI and Vf  would have the unit feet/second.  However, acceleration A has the units  feet/second2 and distance x has the unit feet.  Thus the Ax term would have the units (feet/second2)(feet) or   feet2/second2.  For a formula to be valid it must be dimensionally correct - meaning all the terms in the formula must have the same dimensional properties.  In this example, they do not and this means  the formula can not be correct.  Note that the equation would be dimensionally correct if x is the time that the object experiences the acceleration, instead of the distance.  In that case the term Ax would have the units (feet/second2)  (second) which would have the dimension of feet/second and thus make the formula dimensionally correct.  Be aware, however, that just because a formula is dimensionally correct does not mean that formula is scientifically correct. However, if a formula is NOT dimensionally correct, that means it also is NOT scientifically correct.
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A ball is thrown directly downward, with an initial speed of 7.45m/s, from a height of 30.6m. After what time interval does the ball strike the ground?

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