Math Problem Solver

% Define time intervals and acceleration

T1 = 1.2;

T2 = 2;

T3 = 3.2;

% Define acceleration profile

a = [0 -2.5 -2.5 0];

% Create time vector

t = [0 T1 T2 T3];

% Interpolate the acceleration profile for smoother plot

t_interp = linspace(0, T3, 1000); % More time points for interpolation

a_interp = interp1(t, a, t_interp, 'linear');

% Calculate velocity and position using numerical integration (trapezoidal rule)

v = zeros(size(t_interp));

s = zeros(size(t_interp));

for i = 2:length(t_interp)

v(i) = v(i-1) + a_interp(i)*(t_interp(i)-t_interp(i-1));

s(i) = s(i-1) + v(i-1)*(t_interp(i)-t_interp(i-1)) + 0.5*a_interp(i)*(t_interp(i)-t_interp(i-1))^2;

end

% Plot the results

figure(1);

subplot(3,1,1);

plot(t_interp, a_interp, 'LineWidth', 1.5);

xlabel('Time (s)');

ylabel('Acceleration (m/s^2)');

title('Acceleration');

grid on;

xticks(0:0.5:3); % Set x-axis ticks

xlim([0 3.2]); % Set x-axis limits

ylim([-3 0]); % Set y-axis limits

subplot(3,1,2);

plot(t_interp, v, 'LineWidth', 1.5);

xlabel('Time (s)');

ylabel('Velocity (m/s)');

title('Velocity');

grid on;

xticks(0:0.5:3); % Set x-axis ticks

xlim([0 3.2]); % Set x-axis limits

ylim([0 5]); % Set y-axis limits to ensure velocity starts at 5 and decreases

subplot(3,1,3);

plot(t_interp, s, 'LineWidth', 1.5);

xlabel('Time (s)');

ylabel('Position (m)');

title('Position');

grid on;

xticks(0:0.5:3); % Set x-axis ticks

xlim([0 3.2]); % Set x-axis limits

ylim([0 3]); % Set y-axis limits