Question

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?

Answer 1

@Empty

Answer 2

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

Answer 3

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

Answer 4

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)

Answer 5

`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.

Answer 6

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?

Answer 7

Yes, at the minimum, I think your parameterization must agree on starting and ending points.

start = (e/5, e/5)
end = (1, 1)

Answer 8

ok, so how can I find the bounds ?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

\(-1\le t\le 0\)

Answer 14

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

Answer 15

Np :)