VCE Specialist 3/4 Question Thread!

[Phy124]

Hmm, are you sure b^3, I personally think the question is asking when it changes direction?

i.e. 25/4 s

Part b) Find the time the particle is travelling back towards its original position.

I would interpret this as it asking for the time period in which the object is travelling in the negative direction i.e. back to its original position from being stationary.

To calculate this you would do as b^3 has done by subtracting the time it decelerated to a momentarily stationary position from the total time of acceleration in the negative direction.

Although, I do agree it is worded rather ambiguously and if it was on a VCAA exam it would be open to skepticism, I believe this is the correct interpretation of the question.

I think it should be worded: At what time does the particle REACH its initial position?

But OK

Not quite sure I follow this statement though?

[Jenny_2108]

Part b) Find the time the particle is travelling back towards its original position.

I would interpret this as it asking for the time period in which the object is travelling in the negative direction i.e. back to its original position from being stationary.

I agree, because questions given: 20 seconds which returns particle back to its original position => assumed 20s from the opposite direction to the starting point
If the answer is 12+20=32, the question should be the total time takes the particle to travel back the original position

[soccerboi]

Could somebody explain to me why root of x² = |x| ?
Thanks

[Truck]

Could somebody explain to me why root of x² = |x| ?
Thanks

|x| = + or - x.

If x is 2 for example...

2*2 = 4

If x is -2..

-2*-2 = 4

Therefore (+-2)^2 = x^2, or root(4)=x or +-2=|x| .

[soccerboi]

Oh thanks, i kept thinking that |x| meant just +x and was wondering what happened to the -x. Yeh now i understand

[Jenny_2108]

Oh thanks, i kept thinking that |x| meant just +x and was wondering what happened to the -x. Yeh now i understand

x can be positive or negative but |x| is always positive

[WhoTookMyUsername]

It's funny how one part of one chapter of spec is basically all of physics unit 3 AOS 1 LOL

[pi]

Yeah, VCE physics is a joke.

[Truck]

Yeah, VCE physics is a joke.

Really? Please tell me more about your feelings about Physics, as it is a previously unexplored topic which you have never really gone into specific detail about .

[Jenny_2108]

It's funny how one part of one chapter of spec is basically all of physics unit 3 AOS 1 LOL

Last year I was so scared of this chapter but now I really like kinematics I wish I studied Physics unit 3 LOL

Yeah, VCE physics is a joke.

Really? Please tell me more about your feelings about Physics, as it is a previously unexplored topic which you have never really gone into specific detail about .

Vegemite is a physics hater so you wont get any interests of this subject from him btw

[Mr. Study]

Could someone not do the question but tell me how I should attempt it?

I know we are supposed to transpose the equation and let x be the subject and use the intervals on the y-axis but transposing the equation to let x be the subject seems to be pretty tedious. On my CAS calculator, I get 4 different equations...

Note: The region described in part c is the area enclosed by the y-axis and the line y=3.

I should say this is a 5 mark question ...

[xZero]

I'm a but rusty with the solid of revolution, you have to make x^2 the subject right? Try square rooting the whole equation then expand x out, I got a pretty neat equation for x^2 after transposing.

[chris19021]

Hey could u help me with this question
implicity differentiate y²=3xy+x²

Thanks

[Jenny_2108]

Hey could u help me with this question
implicity differentiate y²=3xy+x²

Thanks

2y dy/dx=2x+3x.dy/dx+3y
dy/dx=(3y+2x)/(2y-3x)

[1i1ii1i]

I have 4 questions could anyone help me please i have a SAC tommorow :/
1. On a cattle station there were p head of cattle at time t years after January 1 2005. The populations naturally increases at a rate proportional to p. every year 1000 head of cattle are withdrawn from the herd.
a) show that dp/dt =kp-1000 where k is a constant
b) If the herd initially had 5000 head of cattle, find an expression for t in terms of k and p
c) the population increased to 6000 head of cattle afte 5 years
i) show that 5k=loge((6k-1)/(5k-1))

2. In the main lake of a trout farm the trout population is N at t days afater 1 January 2005, the number of fish harvested on a particular day is proportional to the number of fish in the lake at that time. Every day 100 trout are added to the lake
a) construct a differentialy equation with dN/dt in terms of N and k where k is a constant
b) originally the trout population was 1000. find an expression for t in terms of K and N
c) If the procedure at the farm remains unchanged find the eventual trout population in the lake

3. The water in a hot water tank cools at a rate proportional to (T-t0) where Tdegrees celcius is the temperature of the water
at time t minutes and To the temperature of the surrounding air. When T is 60 the water is cooling at 1degrees celcius per minute
When switched on the heater supplies sufficient heat to raise the temperature by 2degrees celciuseach minute(neglecting heat loss by cooling) If T =20 when the heater is switched on and To=20
a) construct a differential equation for dT/dt as afunction of T (heating and cooling are both taking place)
b) solve the differential equation
c) find the temperature of the water 30minutes after turning it on

4. The rate of growth of a population of iguanas on an islan is given by dW/dt =0.04W where W is the number of iguana alive after
t years. Initially there were 350 iguanas
i) solve the differential equation
ii)give the value of W when t=50
b) if dW/dT =kW and there are 350 iguanas initially find the value of k if the population is to remain constant
c)a more realistic rate of growth for the iguanas is determined by the differential euqation dW/dT=(0.04-0.00005W)W initially there were 350 iguanas
i) solve the differential equation
II) find the population after 50 years

Any help would be appreciated