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The gravitational force on a baseball: Distance of acceleration before release

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The gravitational force on a baseball is -Fgj(with a ^ over the j) A pitcher throws the baseball with velocity vi (with a ^ over the i) by uniformly accelerating it straight forward horizontally for a time interval change of t = t-0 =t. If the ball starts from rest, through what distance does it accelerate before its release and what force does the pitcher exert on the ball?

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The solution shows the formula and workings to arrive at the answer.

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Because,
v = u + a*t
=> v = 0 + a*t
=> a = v/t
now,
v^2 = u^2 + 2*a*s
=> v^2 = 0(initially rest) + 2*(v/t)*s
=> ...

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