Question

A particle passes through the point
P = (4, 3, −5)
at time
t = 5,
moving with constant velocity
v = 4 i  − 3 j  + k.
Find parametric equations for its motion. (Enter your answers as a comma-separated list of equations.)

Answer 1

Hmph. What class is this for? I'm sure there's a prettier way to do this, but you can muscle through it by splitting it all up into its components... What have you got so far?

Answer 2

\[ \textrm {Well, to get started, you know that your velocities in the}
\\ \ \hat i , \hat j , \hat k \
\\ \textrm{ directions are all exclusive of each other. Hooray!}
\\ \textrm{ So if you separate it into components, you get}
\\ \
\\ v_x = 4 units/s
\\ v_y = -3 units/s
\\ v_z = 1 units/s
\\ \
\\ \textrm{so with that you can set up three equations of motion;}
\\ \textrm {we'll do it in one fell swoop to save time}
\\ \
\\ \textbf v = \frac{d \textbf r }{dt}
\\ \
\\ \int_0^{t} \textbf v dt = \int_{r_o}^r d \textbf r
\\ \
\\ \textbf v t = \textbf r - \textbf r_o
\\ \
\\ \textrm{which you can break up into the three equations for x, y, and z}
\\ \
\\ v_x t = x - x_o
\\ v_y t = y - y_o
\\ v_z t = z - z_o
\\ \
\\ \textrm{You can finally plug in all of the given values}
\\ \textrm{to solve for your initial starting positions (xo, yo, zo), then}
\\ \textrm{rearrange your eqs to be in the form }
\\ \
\\ \\ \textbf r = \textbf v t + \textbf r_o
\\ \
\\ \\ \textrm{There should be three of them; your solutions! }
\]

Answer 3

Oh my gosh, thank you so much! :)
This is vector calculus by the way :p sorry I didn't reply sooner!

Answer 4

Welcome, and none worries :)