Doug R. answered • 8d

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This is one of the standard kinematic equations used in physics to track the motion of an object, neglecting friction. In this equation we have vf (final velocity), vi (initial velocity), a (acceleration), xf (final position) and xi (initial position).

To solve for xi, first subtract vi^2 from both sides, giving:

vf^2 - vi^2 = 2a (xf - xi)

Next, divide both sides by 2a to get

(vf^2 - vi^2) / 2a = xf - xi

Finally, subtract xf from both sides:

(vf^2 - vi^2) / 2a - xf = -xi

But wait! There is one more thing to do. Since we don't normally want a negative sign in front of the variable we are solving for, simply get rid of it by multiplying the terms on each side by -1 and rearrange things a bit to make it look more pleasant:

xi = xf - (vf^2 - vi^2) / 2a

Hope this helps!