Question

write a matlab code to find the following: initial position, initial velocity, and acceleration using the algorithm and information below

time(seconds). height(m) velocity(m/s)

0. 0.2. 2.95

algorithm:

1. Enter data in to arrays.

2. Fit the height data to a 2nd order polynomial.

3. Evaluate the polynomial at enough points to get a smooth curve.

4. Find the velocity model by taking derivative of the height polynomial.

5. Evaluate the velocity polynomial at enough times to get a smooth curve

Answer 1

%%Matlab code for time velocity polynomial
clear all
close all

%all height and time data
t=[0 1 2 3 4 5 6 7 8 9 10];
h=[0.1 1.3 4.2 9.9 16.1 25.2 36.9 50.1 65 80.1 98.1];

%2nd order polynomial fit
pp=polyfit(t,h,2);

%smooth t data
tt=linspace(0,10,101);
%polynomial values
hh=polyval(pp,tt);

figure(1)
%plotting of actual and fitted data
plot(t,h,'r*')
hold on
plot(tt,hh)

xlabel('time')
ylabel('height')
title('time vs. height plot')
legend('Actual data','2nd order polynomial')

%function for height n 2nd order polynomial
syms x
h1(x)=pp(1)*x^2+pp(2)*x+pp(3);

fprintf('\t2nd order polynomial fit for height = ')
disp(vpa(h1,4))

%derivative of the function
v(x)=diff(h1,x);

fprintf('\t2nd order polynomial fit for velocity = ')
disp(vpa(v,4))

%all velocity values

for i=1:length(tt)
    vv(i)=double(v(tt(i)));
end

figure(2)
plot(tt,vv)
xlabel('time')
ylabel('velocity')
title('time vs. velocity plot')

%%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%%%%

Please enter your own data and rerun the code.