Substituting this value in the equation for t gives:

to evaluate C: When t=0, d=0 and therefore

Substituting this expression for C gives the equation for the time, t, required to recoil any distance, d.

Solving this equation for d gives the inverse relation expressing the distance recoiled in any time, t.

, KD+Fo . T /K , , -i v* 1 Fo dā€” K ā€” Sin LVsir +sm KD + FJ" K

Kqnation 1-9 may also be used to obtain the total time T required for the bolt to move through the entire recoil distance D. Substituting D for d gives:

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