close all;
clear all;


%% Symbolic way. It works. But it's not really what Matlab was designed for. Use Maple or Mathematica, etc.
syms time;
syms position;
position = time.^3 - 3*time.^2 - 15*time + 40;
velocity = diff(position, time);
acceleration = diff(velocity, time);
jerk = diff(acceleration, time);
% All in differen sub plots.
figure(1);
tic
subplot(221);
ezplot(position,[0 10]);
title('Position vs Time');
xlabel('Time (s)');
ylabel('Position (m)');
subplot(222);
ezplot(velocity, [0 10]);
title('Velocity vs Time');
xlabel('Time (s)');
ylabel('Position (m/s)');
subplot(223);
ezplot(acceleration, [0 10]);
title('Acceleration vs Time');
xlabel('Time (s)');
ylabel('Position (m/s^2)');
subplot(224);
ezplot(jerk, [0 10]);
title('Jerk vs Time');
xlabel('Time (s)');
ylabel('Position (m/s^3)');
toc
figure(2);

% All on one plot
ezplot(velocity, [0 10]);hold all
ezplot(acceleration, [0 10]);hold all
ezplot(jerk, [0 10]);hold all
ezplot(position,[0 10]); hold all % Put last because EZ plot screws with axes
legend('Position (m)','Velocity (m/s)','Acceleration (m/s^2)','Jerk (m/s^3)');
xlabel('Time (s)');

%% Closer to the a good MatLab way.
figure(3);
tic
time=0:0.01:10;
position1=subs(position);
velocity1=subs(velocity);
acceleration1=subs(acceleration);
jerk1=subs(jerk);
plot(time,position1,time,velocity1,time,acceleration1,time,jerk1);
legend('Position (m)','Velocity (m/s)','Acceleration (m/s^2)','Jerk (m/s^3)');
xlabel('Time (s)');
toc


%% IHO the best.
figure(4);
clear position time;
tic
dt=1e-3;
time=0:dt:10;
position = time.^3 - 3*time.^2 - 15*time + 40;
velocity = diff(position)/(dt)^1;
acceleration=diff(position,2)/(dt)^2;
jerk=diff(position,3)/(dt)^3;
plot(time,position,time(2:end),velocity,time(3:end),acceleration,time(4:end),jerk);
toc