clc
clear

t = 0:0.01:10;               
xA = 0.6 .* t;
xB = 0.05 .* t.^2 + 0.1 .* t + 0.5;

plot(t, xA, 'b-', 'LineWidth', 2);
plot(t, xB, 'r-', 'LineWidth', 2);

meetingTimes = sort(roots([0.05, -0.5, 0.5]));
meetingPositions = 0.6 .* meetingTimes;
plot(meetingTimes, meetingPositions, 'ko', 'MarkerFaceColor', 'k');

xlabel('Time (s)');
ylabel('Position');
title('Position of carts A and B versus time');
legend('Cart A', 'Cart B', 'Where carts pass', 'Location', 'best');
grid on;

fprintf('First meeting: t = %.2f s, x = %.2f\n', meetingTimes(1), meetingPositions(1));
fprintf('Second meeting: t = %.2f s, x = %.2f\n', meetingTimes(2), meetingPositions(2));