%Given Variables
syms qi qf qddc tf;
%Set Given Values
qi=.1;
qf=1.2;
qddc=6;
tf=1.2;

%Check for valid condition
if ((qddc*tf^2)/4<=(qf-qi))
    fprintf("The motion cannot be completed with the given parameters")
    return
end
%Solved Variables
syms tc qdc;
%Variable Relations
eq1=subs(qdc==qddc*tc);
eq2=subs((qf-qi)==(tf-tc)*qdc);
eq3=subs(tc<=tf/2);
%Solving
S=solve([eq1,eq2,eq3],[tc,qdc]);
tc=S.tc;
qdc=S.qdc;
%Define Piecewise Functions
syms x
q=piecewise(0<x<tc, qi+qddc*x^2/2, tc<x<(tf-tc), qi+qddc*tc^2/2+(x-tc)*qdc, (tf-tc)<x<tf, qf-(tf-x)^2*qddc/2);
qd=piecewise(0<x<tc, qddc*x, tc<x<(tf-tc), qdc, (tf-tc)<x<tf, -qddc*(x-tf));
qdd=piecewise(0<x<tc, qddc, tc<x<(tf-tc), 0, (tf-tc)<x<tf, -qddc);
%Plotting
hold on
subplot(3,1,1)
fplot(q, [0 tf])
xlabel('time')
ylabel('Position')
subplot(3,1,2)
fplot(qd, [0 tf])
xlabel('time')
ylabel('Velocity')
subplot(3,1,3)
fplot(qdd, [0 tf])
xlabel('time')
ylabel('Acceleration')