OpenStudy (anonymous):

If a particle moves from point (e/5,e/5) to point (1,1), what is the parametric equation and its bounds? So I subtracted the two and and said: r(t) = (1,1) +t(1-e/5,1-e/5). Is this correct, and what are the bounds?

3 years ago
OpenStudy (jhannybean):

@Empty

3 years ago
ganeshie8 (ganeshie8):

One way to test if it is the correct parameterization is : plug in \(t = 0\) and you should get the starting point

3 years ago
OpenStudy (anonymous):

oh, I get point 1,1, so I assume this is correct then

3 years ago
ganeshie8 (ganeshie8):

Assuming time is a one way road, going from (e/5, e/5) to (1, 1) is not same as going from (1, 1) to (e/5, e/5)

3 years ago
jimthompson5910 (jim_thompson5910):

`If a particle moves from point (e/5,e/5) to point (1,1), what is the parametric equation and its bounds?` How long does it take to go from (1,1) to (e/5, e/5) ? It doesn't state the time t value.

3 years ago
OpenStudy (anonymous):

it does not state the t value. So If time is a one way road, is my equation supposed to be the other way round?

3 years ago
ganeshie8 (ganeshie8):

Yes, at the minimum, I think your parameterization must agree on starting and ending points. start = (e/5, e/5) end = (1, 1)

3 years ago
OpenStudy (anonymous):

ok, so how can I find the bounds ?

3 years ago
ganeshie8 (ganeshie8):

If you fix the bounds to be \(0\le t\le 1\), then you can have an unique linear parameteriation : \(r(t) = (e/5,e/5) +t(1-e/5,1-e/5)\)

3 years ago
OpenStudy (jhannybean):

The form is... I believe \(\sf \mathbf {\vec r} = P_0 +t\mathbf {\vec v}\) where \(\sf P_0\) is the initial starting point.

3 years ago
OpenStudy (anonymous):

so do you just choose 0 and 1 ad fix, or there should be some way to go about it?

3 years ago
ganeshie8 (ganeshie8):

Thats a more natural and easiest way. You could also mess with your original parametric form and get suitable bounds for \(t\)

3 years ago
ganeshie8 (ganeshie8):

Below parameterization works equally well too : \(r(t) = (1,1) +t(1-e/5,1-e/5)\) \(-1\le t\le 0\)

3 years ago
OpenStudy (anonymous):

@Jhannybean ,@Empty ,@Astrophysics ,@imqwerty and @jim_thompson5910 thank you so much for taking some and looking at this. And all the help. Thank you!

3 years ago
OpenStudy (jhannybean):

Np :)

3 years ago