Question

3) Develop a Matlab function to compute the velocity v of a particular projectile as a function of time t. In this problem, the velocity profile is described by a piecewise function, and is parameterized by 11 parameters, a, b, c, d, g, h, k, m, n, p, and q, as at - bt, 05158 c-dt, 851516 v(t;a,b,c,d,g,h,k,m,n, p,q) = gt +h(t – k)?, 1651526 me=n(t-p), > 26 else. Your Matlab function must take as input the current time value and a vector of user arguments relating to particular values of the 11 parameters, a, b, c, d, g, h, k, m, n, p, and q. So, for example, if your function name is vfunc, then your vfunc function must take as input a single value of time, say t, and a vector of user arguments, say user, to yield a velocity value, say v; in this case, the function definition line of your Matlab file, where you define the function, would look like this: function v = vfunct, user) By the way, you are not required to use the function or variable names used above; you are free to name these things how you wish. Test your function by writing a script which incorporates a for loop to step through each value of time in your time vector and calls the velocity profile function with Matlab built-in feval to compute the value of the velocity profile

Answer 1

• clc
  clear all
  close all
  a=10;
  b=5;
  c=624;
  d=3;
  g=36;
  h=12;
  k=16;
  m=2136;
  n=0.1;
  p=26;
  q=0;
  user=[a,b,c,d,g,h,k,m,n,p,q];
  t=-5:0.01:50;
  v=[];
  for i=1:length(t)
  v(i)=vfunc(t(i),user);
  end
  plot(t,v);
  xlabel('Time');
  ylabel('v(t)');
  title('Plot of v(t)');
  function v=vfunc(t,user)
  a=user(1);
  b=user(2);
  c=user(3);
  d=user(4);
  g=user(5);
  h=user(6);
  k=user(7);
  m=user(8);
  n=user(9);
  p=user(10);
  q=user(11);
  v=0;
  if(t>=0&&t<=8)
  v=a*t^2-b*t;
  elseif(t>=8&&t<=16)
  v=c-d*t;
  elseif(t>=16&&t<=26)
  v=g*t+h*(t-k)^2;
  elseif(t>26)
  v=m*exp(-n*(t-p));
  else
  v=q;
  end
    
  end