I didn't clean up the code. But more or less, the hold is used. You can also set the LineColor so that it appears as a piecewise function.
Xu=linspace(0,12,60);
Yu=linspace(0,10,60);
plot(Xu,Yu, 'LineWidth', 1.5), hold on
% xlabel('temps(min)')
% ylabel('X(km)')
% p1.LineWidth = 1.5;
% grid on
%----------
Xu=linspace(12,24,60);
Yu=linspace(10,0,60);
plot(Xu,Yu, 'LineWidth', 1.5), hold on
% xlabel('temps(min)')
% ylabel('X(km)')
% p1.LineWidth = 1.5;
% grid on
%-------------------
Xu=linspace(24,36,60);
Yu=linspace(0,10,60);
plot(Xu,Yu, 'LineWidth', 1.5), hold on
% xlabel('temps(min)')
% ylabel('X(km)')
% p1.LineWidth = 1.5;
% grid on
%----------------
Xu=linspace(36,48,60);
Yu=linspace(10,0,60);
plot(Xu,Yu, 'LineWidth', 1.5), hold on
% xlabel('temps(min)')
% ylabel('X(km)')
% p1.LineWidth = 1.5;
% grid on
%-------------
Xu=linspace(48,60,60);
Yu=linspace(0,10,60);
plot(Xu,Yu, 'LineWidth', 1.5), hold off
xlabel('temps(min)')
ylabel('X(km)')
grid on
