function [ t] = part4( s )
tal = 2.495246747676093; % Total arc length
%s = input('input the fraction of the curve you would like to know the time value for: ');
tol=1e-6;
%  x = x-f(x)/df(x)
f =@(t) sqrt((.3+7.8*t-14.1*t^2)^2+(.3+1.8*t-8.1*t^2)^2);
t_vec=.5;
t = t_vec; df = f(t);
t_vec(2) = t - (adapquad(f_t,0,t,tol)-s*tal)/df;
%x = x- func/dfunc
% f_t = sqrt((.3+7.8*t-14.1*t^2)^2+(.3+1.8*t-8.1*t^2)^2)
i=1;
while abs(t_vec(i+1)-t_vec(i))>1e-5
    i = i+1;
    t = t_vec(i);
    df = f(t);
    t_vec(i+1) = t - (adapquad(f_t,0,t,tol)-s*tal)/df;
end

partial_arc = adapquad(f_t,0,t,1e-6);
Arc_length_over_partial = partial_arc/tal;
end