easy motion (1 Viewer)

[sasquatch]

ok i dont really have any problems but i think the books answers is wrong. just want to make sure is all.

A particle moves in a straight line in such a way that its distance, x meters from a fixed point O, in the line after t seconds is given by x = 4t - 5t² + 2t³.

Find:
d) The time when v = 0
e) The acceleration euqation and calculate the velocity when the acceleration is zero.

Thanks to anybody who helps out.

 

[Triangulum]

a) v = dx/dt = 4 - 10t + 6t²

So v = 0 when
6t² - 10t + 4 = 0
(t - 1)(6t-4) = 0
t - 1 = 0 or 6t - 4 = 0

t = 1 or t = 2/3

So velocity is 0 m/s when t = 1s or t = 2/3s

b) a = d²x/dt² = dv/dt = -10 + 12t = 12t - 10

When a = 0
12t - 10 = 0
t = 5/6s

When t = 5/6
v = 4 - (10 x 5/6) + 6 x (5/6)²
v = - 1/6

So when acceleration is 0 m/s², velocity is -1/6 m/s.


I think that's all right, but I may be wrong somewhere.

 

[sasquatch]

Yeah i got the same as what you had triangle dude. pLuvia, you made a small mistake, you divided incorrectly. Also could somebody please check this out.. i swear this book is screwy...

Q2. The distance x meters at time t seconds of a particle moving in a straight line from a fixed point is given by x = 2 - 2cos2t.

a) Sketch the graph of this equation for 0 <= t <= 2pi
b) Find the times wehre the particle is at rest and where the particle is at these times.
c) What is the maximum distance of the particle from O.

This is what i did:
a) Well cant really draw it here..

b) v = dx/dt = -2 * -sin2t * -2
= 4sin2t

Particle is at rest when v = 0,

so sin2t = 0,
2t = 0, pi, 2pi, 3pi, 4pi.

hence t = 0, pi/2, pi, 3pi/2, 2pi.

If t = 0, x = 0m
If t = pi/2, x = 4m
If t = pi, x = 0m
If t = 3pi/2, x = 4m
If t = 2pi, x = 0m

c) From the graph, the max distance from point O is 4m.

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The answer in the back has this answer for 2b,

t = 21pi/36, 5pi/6; x = 3.73, x = 1.5.

I have no idea where thats from, and there is no answer to part c.

Thanks alot!

 

[Triangulum]

I'd do those ones as well, but anything involving both calculus and trig will just make me want to cry (it's my pet hate), so I won't.

 

[sasquatch]

Umm hehe ok well thanks for helping me anyway!

 

[SoulSearcher]

sasquatch, you seem to have the correct answers, I have no idea how the book got its answers for 2b)

 

[Riviet]

Yeah, that all looks correct, don't have a clue how the textbook ended up with an exact value of 21pi/36 and it's not even fully simplified!

 

[sasquatch]

This book is making me feel crappy.. again i have the wrong answer...dunno why though..

So if anybody doesnt mind..could you check this... sorry.... Thanks though to everyone who has contributed.

A particle moves along the x axis with an acceleration given by a = 6t + 3. When t = 0, x = 5 and the velocity of the particle is 1 unit pers second. Find the position of the particle after 3 seconds.

a = 6t + 3
v = 6t²/2 + 3t + c

but if t = 0, v = 1,

1 = c

.:. v = 3t² + 3t + 1

x = 3t³/3 + 3t²/2 + t + d

but if t = 0, x = 5

5 = d

.:. x = t³ + (3/2)t² + t + 5

When t=3,

x = 27 + (3/2)(9) + 3 + 5
=48.5 units

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But the answer is x = 21.5

i hate this book!

 

[Riviet]

Once again I don't see any holes in your working.

P.S Does this book happen to be Fitzpatrick?

 

[SoulSearcher]

All looks fine from here. What book are you using?

 

[sasquatch]

Nope not fitzpatrick, im using jones and couchman. The weird thing is though, i have never encountered so many errors like so close together before. Motion and physicy stuff must be their weak area then.. hehe..

 

[Triangulum]

Nope not fitzpatrick, im using jones and couchman. The weird thing is though, i have never encountered so many errors like so close together before. Motion and physicy stuff must be their weak area then.. hehe..

We use Jones and Couchman as well, and their error rate is pretty high everywhere. They also have no consistency in how they present their answers, which is irritating, but also irrelevant to this topic. Shall I stop rambling?