format short
clear all
clc
Speed_first=@(t)0.1553567*(t.^6)-2.0416*(t.^5)+9.1837*(t.^4)-14.829*(t.^3)-1.3703*(t.^2)+32.821*t-1.3155;
Speed_second=@(t)0.003980879*(t.^5)-0.2247*(t.^4)+4.8682*(t.^3)-50.442*(t.^2)+254.67*t-430.66;
Speed_third=@(t)-0.073*(t.^2)+6.1802*t+40.423;
time=0:0.01:25;
speed=[];
l=length(time);
for i=1:l
if (time(i)<5)
speed(i)=Speed_first(time(i));
elseif (time(i)<15.4)
speed(i)=Speed_second(time(i));
else
speed(i)=Speed_third(time(i));
end
end
subplot(2,1,1)
plot(time,speed)
ylabel('Speed')
xlabel('Time')
title('Time against speed')
N=2;
Er = 100;
old_integral = 100;
Number_sections=[];
Integrals=[];
while Er > 0.00002
[integral,Distance_vec,time_vec]=inttrapezoidal(N);
Number_sections = [Number_sections N];
Integrals = [Integrals integral];
N = N*2;
Er=abs(((integral-old_integral)/integral)*100);
old_integral=integral;
fprintf('\n Integral= %g; number of Sections = %g; Relative Error = %f\n',integral,N, Er)
end
subplot(2,1,2)
plot(time_vec, Distance_vec);
title('Cumulative distance by time');
xlabel('Time');
ylabel('Distance travelled');
figure()
semilogx(Number_sections,Integrals);
title('Distance travelled by number of sections');
xlabel('Number of Sections');
ylabel('Distance travelled');
function [integral,Distance_vec,time_vec] = inttrapezoidal(N)
a = 0;
b = 25;
h = (b-a)/N;
Distance_vec(1) = 0.0;
for m = 2:N
x_left = a+(m-1)*h;
x_right = a+m*h;
f_left = f(x_left);
f_right = f(x_right);
Distance_vec(m) = Distance_vec(m-1)+h/2*(f_left+f_right);
time_vec(m)=x_left;
end
integral=Distance_vec(end);
end
function v = f(time)
if time<=5
Speed = 0.1553567*(time.^6)-2.0416*(time.^5)+9.1837*(time.^4)-14.829*(time.^3)-1.3703*(time.^2)+32.821*time-1.3155;
elseif time>=5 && time<15.4
Speed = 0.003980879*(time.^5)-0.2247*(time.^4)+4.8682*(time.^3)-50.442*(time.^2)+254.67*time-430.66;
else
Speed =-0.073*(time.^2)+6.1802*time+40.423;
end
v=Speed*0.47404;
end
