MATLAB: My code is just about there, but there is something not right…I can’t figure it out. Help?!

for loopif statementphysics

Here's my code:
if true
  % code
end
m=1428.8;
a_i=3;
b=1.04;
MaxSpeed= 65 * .4474;
SpeedLimit= 50 * .4474;
t=[0:.5:50];
a= NaN(length(t),1);
v= NaN(length(t),1);
x= NaN(length(t),1);
a(1)=a_i;
v(1)=0;
x(1)=0;
for k = 2:length(t)
  v(k)= a.*t;
  %a)
  if v(k)==min(v(k),MaxSpeed);
      a=0;
      x(k)=v*t(k);
  end
  %b)
  if x(k-1)<275
      a(k)=(b*(v(k-1)).^2)/(2*m);
      x(k)=(MaxSpeed*t)+ (.5*a(k)*(t(k)^2));
  end
  %c)
  if x==1000
      if v(k)>SpeedLimit
          disp('keep coasting');
          v(k)
      end
  end
end
subplot(1,3, 1);
plot(t, x);
xlabel('time(s)');
ylabel('distance(m)');
subplot(1,3, 2);
plot(t, v);
xlabel('time(s)');
ylabel('velocity(m/s)');
subplot(1,3, 3);
plot(t, a);
xlabel('time(s)');
ylabel('acceleration');

Best Answer

I am pretty sure this is the correct code now. As for the sum(x>1000), the answer was 44. Is that the number of time steps it took for x to become greater than 1000? Here's the code:
m=1428.8;%mass of car
  a_i=3;%initial acceleration
  b=1.04;%constant
  MaxSpeed= 65 * .4474;%mph - m/s

  SpeedLimit= 50 * .4474;%mph - m/s
  dt=.5;%time step
  t=[0:dt:50];%time
  N=length(t);%legthg of time
  a= NaN(1,length(t));%empty acceleration vector
  v= NaN(1,length(t));%empty velocity vector
  x= NaN(1,length(t));%empty position vector
  a(1)=a_i;%initial acceleration = 3
  v(1)=0;%initial velocity = 0
  x(1)=0;%initial position =0 
  for k=2:N
      F_drag=.5*b*((v(k-1))^2);%drag force 
      a(k)=a(k-1)-(F_drag/m);%net acceleration 
      v(k)= v(k-1)+ ((a(k)+a(k-1))/2)*dt;%velocity 
      x(k)=x(k-1)+ dt*((v(k)+v(k-1)/2));%position 
      %a)
      if x(k)>150%when acceleration should equal zero 
          a(k)=0;%acceleration = 0
          v(k)=MaxSpeed;%velocity equals max speed
          x(k)=x(k-1)+ dt*((v(k)+v(k-1)/2));
      end
      %b)
      if x(k-1)>275%when you pass the 50mph speed limit sign
          a(k)=-(F_drag/m);%acceleraton from the car is zero and the drag force is decelerating the car
          v(k)= v(k-1)+ ((a(k)+a(k-1))/2)*dt;%new velocity
      end
  end
    %c)
    if x(k-1)>1000 && v(k)<=SpeedLimit %when you pass the police car
        disp('keep coasting');%if the velocity os less than or equal to the speed limit
        v(k);
        speed=v(k)/.4474;
        disp('speed in mph');
        speed%displays velocity right after you pass the police car
    else
        disp('pull over');%if velocity is greater than the speed limit
        v(k);
        speed=v(k)/.4474;
        speed
    end
    figure;%plots
    subplot(3,1, 1)
    plot(t, x)%time vs. position plot
    xlabel('time(s)');
    ylabel('position(m)');
    subplot(3,1, 2)
    plot(t, v)%time vs. velocity
    xlabel('time(s)');
    ylabel('velocity(m/s)');
    subplot(3,1, 3)
    plot(t, a)%time vs. acceleration plot
    xlabel('time(s)');
    ylabel('acceleration');
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