Question

The position function x(t) of a particle moving along an x axis is x=4.0 - 6.0t^2, with x in metres and t in seconds. (a) At what time and (b) where does the particle (momentarily) stop? At what (c) negative time and (d) positive time does the particle pass through the origin? (e) Graph x versus t for the range -5 s to +5 s. (f) To shift the curve rightward on the graph, should we include the term +20t or the term -20t in x(t)? (g) Does that inclusion increase or decrease the value of x at which the particle momentarily stops? I already did (a) and (b) and (e). I need help with the rest.

Answer 1

to me the origin is 0,0. According to the xlsx enclosed the thing doesn't go through the origin ???

Answer 2

modified spreadsheet encl.
SHOULD now be three sheets ...

plus 20 t.
increases

Answer 3

(a) At what time ....

\( x=4 - 6t^2, \dot x = - 12t = 0\), and \(\dot x = 0 \implies t = 0\),


and (b) where

\(t = 0 \implies x = 4\)


does the particle (momentarily) stop?

At what (c) negative time ...

\(x = 4 - 6t^2\) so \(x = 0 \implies t = \pm \sqrt{ \dfrac{2}{3} }\)

So: \( t = - \sqrt{ \dfrac{2}{3} }\)


and (d) positive time does the particle pass through the origin?

So: \( t = \sqrt{ \dfrac{2}{3} }\)


(e) Graph x versus t for the range -5 s to +5 s.



(f) To shift the curve rightward on the graph, should we include the term +20t or the term -20t in x(t)?

to shift rightward write it as: \( x=4 - 6(t-20)^2\)


(g) Does that inclusion increase or decrease the value of x at which the particle momentarily stops?

Shifting right means particle now stops at \(t = 20\)

Check it:

\( x=4 - 6(t-20)^2\)

\( \dot x=- 2*6(t-20) = 0 \implies t = 20, ~ x = 4 \)

Answer 4

@IrishBoy123 Very elegant expo. and expl. At least I got the graph right !

Answer 5

thank you mate !!

you can report me for feeding answers, if you like :)

Answer 6

Done.

Answer 7

arsehøle! i still haven't got an email.

I might just have to do it myself.

Answer 8

https://www.youtube.com/watch?v=GOkZs2RZMQY&list=PLD29CE3C0885891C7&index=10

FWIW: i recommend this, highly. an uber-genius at work.

@osprey: Legendre :)

Answer 9

Offensive..

Answer 10

@S4Sensitiveandshy

FYI, i found the thing below deeply "offensive". I reported it twice, in each case well before it was announced that this ship had officially hit the iceberg.



Yet still Nada.

Answer 11

I need glasses to read that

Answer 12

Gone.

Answer 13

@S4Sensitiveandshy
well, yes and no you need glasses. If you save the pic and then read it it's larger.
@IrishBoy123
But, then, I think I've seen the post before, so it's there in "larger print" somewhere else.

Answer 14

it's legible even on a smartphone. i've tested it


and here is a png link

https://i.gyazo.com/7e2558c11de97c9727ec5ddf62fb433a.png

the original thread is still out there too but the lag here makes it a pain to find.

Answer 15

found it:

http://openstudy.com/updates/5810b82ae4b075d6916f6fd1

Answer 16

@IrishBoy123
the original thread is still out there too but the lag here makes it a pain to find.
Yup; agreed, totally agreed.

Answer 17

this is my smartphone. http://prnt.sc/df8ny5

Answer 18

Thanks for the link. I was looking for the thread too, but..i gave up.... because of the lag....

Answer 19

thanks @S4Sensitiveandshy .