%*** CHAPTER 9: TRAJECTORY GENERATION ***

function s = CubicTimeScaling(Tf, t)
% Takes Tf: Total time of the motion in seconds from rest to rest,
%       t: The current time t satisfying 0 < t < Tf.
% Returns s: The path parameter s(t) corresponding to a third-order 
%            polynomial motion that begins and ends at zero velocity.
% Example Input: 
%{
  clear; clc;
  Tf = 2;
  t = 0.6;
  s = CubicTimeScaling(Tf,t)
%}
% Output:
% s =
%    0.2160

s = 3 * (t / Tf) ^ 2 - 2 * (t / Tf) ^ 3;
end