Applications of Calc. 2 r.world question (1 Viewer)

[Mc_Meaney]

Hey guys, I am in need of some help

I am struggling with a couple of questions, and ive only just started the topic
\
"If the velocity of the particle, after t seconds moving in a straight line is
given by v= 10 + 6t - t² find the acceleration when t=2 and the greatest possible velocity attained bby the particle

a) This is my working, i think its correct by not certain

acc = dv/dt
= 6-2t
At t=2, a = 2

b) Im havinng trouble working this one out

TY in advanced

 

[karnoganguli]

(a) is correct i believe

(b) dv/dt = 6- 2t
dv/dt= 0
6-2t= 0
t= 3

sub 3 into 10+6t- (t^2)= 19m/s
90% sure this is correct... could someone check this

 

[Mc_Meaney]

I have a new question (suprise suprise)

a part. is moving in a str8 line iso that its distance (x) awyas from O (origin) after t seconds is given by x=12t-t³

1. Sho its at the origin intitally and find its int. velocity.

(Sub 0 done) (differentiate and sub 0 done) affter 0 secs, int velocity is 12m/s

2. Show it moves away from O for 2 secs then it returns at 24jm/s in the negative direction

I dont know how to do this, and the text book (in the Couchman wisdom) doesnt have an answer!....but i think this is what i do....

0=12-3t²
t=2

Returns to 0 at t=3...(i think) and thats where i get stuck...is my working right, and how do i go about finishing it off...with or without that working.

Thanx again

 

[SoulSearcher]

You're on the right track. First you had to show that there was a turning point at t = 2, and then find the velocity when the particle goes back to the origin, i.e.
0 = 12t - t³
t(12-t²) = 0
Therefore t = 0 or t = rt12
Finding the velocity at t = rt12,
v = 12 - 3(rt12)²
= 12 - 36
= -24m/s, therefore the particle has a velocity of 24m/s in the opposite direction when it returns to the origin.

 

[dddman]

Yes that is entirely true.

When acceleration = 0 , velocity is at max (or min, depending on the sign of the x² term, but in this case, it's a max).

WRONG! ur assuming it is at its max

for b) you need to deferinate it again and prove that D^2V/T^2 is <0

as D^2V/T^2 = -2, you will not get the full marks if u assume shit

 

[Mc_Meaney]

Yeh....i have another question....well two really.

"The decay of radium is proportional to its mass. if 100kg of rad. takes 5 years 2 decay to 95kg...."

Using M=100e^-0.01t

(b) find its mass after 10 years

(c) find its half life

I key coming up about .5 short, and i dunno if im doing the write working out or if the book is wrong.

 

[SoulSearcher]

Are you using the exact value of k when you calculate the mass and the half-life? Unless told otherwise, always use the exact value when doing calculations such as these.

 

[Mc_Meaney]

The value of k is given as -0.01

 

[SoulSearcher]

Hmm maybe then they or you are just rounding off wrong.

 

[Mc_Meaney]

Hmm maybe then they or you are just rounding off wrong.

im keep getting it wrong by .5, its not a matter of rounding

 

[SoulSearcher]

Fine, I'll do the question, see what answers I get.
Using M = 100e^-0.01t
When t = 10,
M = 100e^-0.1
= 90.4837418...
= 90.48 grams to 2 dec. places
The length of the half-life is found when M = 50
50 = 100e^-0.01
0.5 = e^-0.01t
-0.01t = ln 0.5
t = [ln(0.5)]/(-0.01)
= 69.31471806...
= 69.31 years to 2 dec. places.

 

[Mc_Meaney]

Same answers i got. Answers are off by about .5

thanx

 

[SoulSearcher]

Then the answers at the back of the book must be wrong

 

[bananasmoothy]

Yeh....i have another question....well two really.

"The decay of radium is proportional to its mass. if 100kg of rad. takes 5 years 2 decay to 95kg...."

Using M=100e^-0.01t

(b) find its mass after 10 years

(c) find its half life

I key coming up about .5 short, and i dunno if im doing the write working out or if the book is wrong.

Isn't this a question from Maths in Focus? Because if it is, then the answer in the back is right...

 

[Mc_Meaney]

It is a MIF question. I cant get the answer in the back, how did u work it?

 

[pLuvia]

Yeh....i have another question....well two really.

"The decay of radium is proportional to its mass. if 100kg of rad. takes 5 years 2 decay to 95kg...."

Using M=100e^-0.01t

(b) find its mass after 10 years

(c) find its half life

I key coming up about .5 short, and i dunno if im doing the write working out or if the book is wrong.

b)When t=10
M=100e^-0.1
=90.48

c)When M=50 t=?
Initial mass is 100
50=100e^-0.01t
1/2=e^-0.01t
ln(1/2)=-0.01t
t=69.31

 

[Mc_Meaney]

That is exactly my working, the book wants 90.25g and 67.6years.

 

[SoulSearcher]

Those answers the book has got using the exact value of k, which is -0.010258658...

 

[Mc_Meaney]

god damnit

 

[Mc_Meaney]

I have a quick question unrelated to this topic but yeh.

Find the exact value of Tan60+Tan150

So Ive got to here:

3^1/2-3^-1/2

Do I need to go further and rationalise the denominator? And if yes, do I apply what I do to the denomator to the _/3 as well?

Sorry, stupid question but I cant remember!

Thanx