VCE Specialist 3/4 Question Thread!

[zsteve]

If you want to interpret it graphically, that would be correct.
For instance, you may say that 'v asymptotically approaches [terminal velocity]', or more mathematically


"The particle decelerates exponentially with terminal velocity k m/s ".
Just on top of Rui's interpretation, I'd add:
Decelerates 'exponentially' with 'terminal velocity' hints that the limiting acceleration is zero, hence \(a = Ae^{-bt}\) is the general form of acceleration (no additive constant because as \(t\to\infty\), \(a\to 0\))

Then I'd integrate to find velocity:


(Above, we solved for C = k due to the limiting condition on velocity)

[knightrider]

If you want to interpret it graphically, that would be correct.
For instance, you may say that 'v asymptotically approaches [terminal velocity]', or more mathematically


"The particle decelerates exponentially with terminal velocity k m/s ".
Just on top of Rui's interpretation, I'd add:
Decelerates 'exponentially' with 'terminal velocity' hints that the limiting acceleration is zero, hence \(a = Ae^{-bt}\) is the general form of acceleration (no additive constant because as \(t\to\infty\), \(a\to 0\))

Then I'd integrate to find velocity:


(Above, we solved for C = k due to the limiting condition on velocity)

Yep i understand now , Thanks so much zsteve  !!!

[blacksanta62]

Hey guys, I'm really struggling with applications of diff. equations and would love some help with these questions:
1) The attachment - how would I do this?
2) Are applications assessed largely in the end of year exam? Like, would they be an extended response question or exam one question. I know that no one here is on the exam panel but just some indication on the difficulty of their questions would be nice.
3) Will exposing myself and practicing enough of these questions make me better at them?

Thank you

[blacksanta62]

Hey guys, this is something that is bugging me and it might be a conceptual misunderstanding. Why is it that we take out a 1/2 as a factor? I thought that we only did that the make the numerator and the value of a the same (but if the numerator was one, then that wasn't needed). So I ended up getting:
x = tan^-1(y + 2/2) +c
and y(0) = 0 ===> c = -pi/4

If anyone could tell me why my way of thinking resulted in a wrong answer and how I should go on about these questions in the future, that would be greatly appreciated

[HighTide]

Hey guys, I'm really struggling with applications of diff. equations and would love some help with these questions:
1) The attachment - how would I do this?
2) Are applications assessed largely in the end of year exam? Like, would they be an extended response question or exam one question. I know that no one here is on the exam panel but just some indication on the difficulty of their questions would be nice.
3) Will exposing myself and practicing enough of these questions make me better at them?

Thank you

I'll just give you the steps for you to try. In this case:
1. Flip to get dt/d(theta) since your function is in terms of theta.
2. Now integrate.
3. Solve for c. There's numerous ways you can do this, Alternatively you can solve for c then solve for theta. Either way just sub in the value of t=0, theta=300 and you'll get a value for c.
4. Solve the equation for theta.
5. Sub in t=10, and you'll get the theta value which is your temperature.
Steps  3 and 4 are interchangeable depending on which method you use.
Give it another try, if you don't understand it I'll provide working.
Other than that, yes you needa know how to do these. They'll defs be in exam 1 and 2.  Yep, expose yourself to them, and that should work. It's initially hard to understand but it gets easier with practice.

[smiley123]

How do I change 7334605/(1476e^-0.833t +2069) into this form A/(1+Ce^-kt)?

[RuiAce]

How do I change 7334605/(1476e^-0.833t +2069) into this form A/(1+Ce^-kt)?

[smiley123]

Yes that was I did, but when I graph it I get a different y-intercept, it's a different dilation. So is it still right?

[zsteve]

Pretty sure Rui's working is correct, but if you get a different graph then whatever it is you graphed is not correct. Perhaps check if you've entered it into the calc correctly?

[Elizawei]

Hey guys, I need a little bit of help 

A container is represented by the diagram below and is given the equation of y=4/7x^2+3/7

Find V (volume of water in litres) as a function of the height (h metres), above the floor

I'm not too sure how to express V in terms of h Does this question involve rotations?
Thanks!

[Callum@1373]

Hey guys, I need a little bit of help 

A container is represented by the diagram below and is given the equation of y=4/7x^2+3/7
(Image removed from quote.)
Find V (volume of water in litres) as a function of the height (h metres), above the floor

I'm not too sure how to express V in terms of h Does this question involve rotations?
Thanks!

I think you would have to do the integral with upper limit as "h" and lower limit as 1, rotated about the y axis

[Elizawei]

I think you would have to do the integral with upper limit as "h" and lower limit as 1, rotated about the y axis

Hmm alrighty thanks!!

[Callum@1373]

Hey, does anyone know where I can find some difficult problem solving questions on topics for DE's/integration/kinematics/vector calc asides from itute exams?

[lzxnl]

Hey, does anyone know where I can find some difficult problem solving questions on topics for DE's/integration/kinematics/vector calc asides from itute exams?

If you want harder integrals, google 'difficult integrals'. I legit did that one day and the integrals I got weren't easy. Try http://www.physicsforums.com/showpost.php?p=3433157&postcount=272 for instance.

As for the others, if you've worked through the Essentials book for spesh (I know, it's a bit old, but that's what I used), it's really good.
The questions they can ask you on vector calc are pretty limited; probably more important you're comfortable with vectors and geometric proofs with vectors tbh. Vector calc questions tend to be vector questions except the vectors depend on time or something now.

[blacksanta62]

I'll just give you the steps for you to try. In this case:
1. Flip to get dt/d(theta) since your function is in terms of theta.
2. Now integrate.
3. Solve for c. There's numerous ways you can do this, Alternatively you can solve for c then solve for theta. Either way just sub in the value of t=0, theta=300 and you'll get a value for c.
4. Solve the equation for theta.
5. Sub in t=10, and you'll get the theta value which is your temperature.
Steps  3 and 4 are interchangeable depending on which method you use.
Give it another try, if you don't understand it I'll provide working.
Other than that, yes you needa know how to do these. They'll defs be in exam 1 and 2.  Yep, expose yourself to them, and that should work. It's initially hard to understand but it gets easier with practice.

Thank you