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

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Jacob Savona
Jacob Savona 2015-2-23
回答： Jacob Savona 2015-2-24
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');
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采纳的回答

Jacob Savona
Jacob Savona 2015-2-24
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');

更多回答（3 个）

Rick Rosson
Rick Rosson 2015-2-23
编辑：Rick Rosson 2015-2-23
The very first line inside the for loop is not correct:
v(k)= a.*t;
First of all, you need to define a time increment before you even get to the for loop:
dt = 0.5;
Then, inside the for loop, you can compute the velocity at the current time step as a function of the velocity and acceleration at the previous time step:
v(k) = v(k-1) + dt*a(k-1);
and the position in a similar fashion:
x(k) = x(k-1) + dt*v(k-1);
Then, you need to compute the drag as a function of the velocity:
F_drag = ...
Then, the net force as the sum of the applied force and the drag:
F_net = F_applied + F_drag;
(assuming that the drag force is opposite in sign as the velocity; otherwise, change the '+' sign to a '-' sign in the above expression).
Finally, you can compute the net acceleration using Newton's second law:
a(k) = F_net / m ;
Does that make sense?
Please try to modify your code, and then re-post it here with specific questions if you still need help.
Rick
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Image Analyst
Image Analyst 2015-2-24
Jacob's comment moved here:
So now I have acceleration to equal zero when the velocity is MaxSpeed, but only in that instant of time. I know I have to change the acceleration equals from that point on, but I'm unsure how to do it...
Here's the new code:
for k=2:N
F_drag=.5*b*((v(k-1))^2);
a(k)=a(k-1)-(F_drag/m);
v(k)= v(k-1)+ (a(k)+a(k-1))*dt;
v(k)=min(v(k),MaxSpeed);
j=k(find(v(k)== MaxSpeed));
a(j)=0;
x(k)=x(k-1)+ dt*(v(k)+v(k-1));
end

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Jacob Savona
Jacob Savona 2015-2-23
编辑：Jacob Savona 2015-2-23
Thank you for the advice, I'm am new to the forum...obviously. I attempted part a). The problem is with the acceleration. The initial acceleration at t=0 is 3, but after that a=3-Fdrag. At the time v=65mph or MaxSpeed, a=0. Here's what I got:
if true
% code
end
m=1428.8;
a_i=3;
b=1.04;
MaxSpeed= 65 * .4474;
SpeedLimit= 50 * .4474;
dt=.5;
t=[0:dt: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)
F_drag=.5*b*(v(k-1))^2;
a(k)=a(k-1)-F_drag;
v(k)= v(k-1)+ dt*a(k-1);
x(k)=x(k-1)+ dt*v(k-1);
%a)
if v(k)==min(v(k),MaxSpeed);
a=0;
x(k)=MaxSpeed*t(k);
end
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Rick Rosson
Rick Rosson 2015-2-24
编辑：Rick Rosson 2015-2-24
Take a look at how Image Analyst solved this part of the problem in his answer to your earlier question. Notice that he did not use an if statement. Also notice where he put the line of code to adjust for the maximum speed.
Jacob Savona
Jacob Savona 2015-2-24
I don't understand why the if statement to make the acceleration to equal 0 when the velocity is the MaxSpeed doesn't work.
New Code:
for k=2:N
F_drag=.5*b*((v(k-1))^2);
a(k)=a(k-1)-(F_drag/m);
v(k)= v(k-1)+ (a(k)+a(k-1))*dt;
v(k)=min(v(k),MaxSpeed);
j=k(find(v(k)== MaxSpeed));
a(j)=0;
if a(k)==0
a(k)=0;
v(k)=MaxSpeed;
end
x(k)=x(k-1)+ dt*(v(k)+v(k-1));
end

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Jacob Savona
Jacob Savona 2015-2-24
My code is now working, but it won't display in the if statement at c) and the plots won't display either. I don't understand, does it mean the loop isn't being finished?
Code:
m=1428.8;
a_i=3;
b=1.04;
MaxSpeed= 65 * .4474;
SpeedLimit= 50 * .4474;
dt=.5;
t=[0:dt:50];
N=length(t);
a= NaN(1,length(t));
v= NaN(1,length(t));
x= NaN(1,length(t));
a(1)=a_i;
v(1)=0;
x(1)=0;
for k=2:N
F_drag=.5*b*((v(k-1))^2);
a(k)=a(k-1)-(F_drag/m);
v(k)= v(k-1)+ (a(k)+a(k-1))*dt;
x(k)=x(k-1)+ dt*(v(k)+v(k-1));
%a)
if x(k)>150
a(k)=0;
v(k)=MaxSpeed;
end
%b)
if x(k-1)>275
F_drag=.5*b*((MaxSpeed)^2);
a(k)=a(k-1)-(F_drag/m);
v(k)= v(k-1)+ (a(k)+a(k-1))*dt;
end
%c)
if x(k)>1000
if v(k)>SpeedLimit
disp('keep coasting');
disp(v(k));
else
disp('pull over');
disp(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');
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Rick Rosson
Rick Rosson 2015-2-24
BTW, the third line inside the for loop is definitely not correct:
v(k)= v(k-1)+ (a(k)+a(k-1))*dt;
If you are going to use the acceleration at both the current time step and the previous time step, you should at least divide by 2 so that you take the average rather than the sum:
v(k)= v(k-1)+ ((a(k)+a(k-1))/2)*dt;
Rick Rosson
Rick Rosson 2015-2-24
You have made a lot of excellent progress. Don't give up. You are much closer than you were yesterday. A few minor tweaks and you can get to the right solution.

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