Computer Programming/Physics/Position of an accelerating body function

Wikisource:Source code The position of an accelerating body can be described by a mathematical function . The generalized function can be attained by using the Taylor series , where is the derivative of : etc. The accuracy of this function depends on the number of terms used as decreases rapidly. Additionally, the time can be synchronized such that (Maclaurin series). Note that for a constant acceleration most of the terms become zero and we're left with or C++ template<class Vector,class Number> Vector PositionAcceleratingBody(Vector *s0,Number t,size_t Accuracy) { Vector s(0); //set to zero if int, float, etc. or invoke the // "set to zero" constructor for a class Number factor(1);//0!==1 and t^0==1 for(size_t n(0);n<Accuracy;n++) { if(n)factor*=(t/n);//0!==1 and t^0==1 s+=(factor*s0[n]); //s0 is the array of nth derivatives of s // at t=t0=0 } return s; } Justification for Using the Taylor Series The Taylor series can be derived by systematically selecting which of our variables is a constant and then extrapolating that to the infinite limit. Constant Position or Constant Velocity or Constant Acceleration or Constant Rate of Change of Acceleration or etc.