Question

a(t) = A + Bt

x(0) =xi

v(0) = vi

derive the position as a function of time equation

Answer 1

take the first integral

v(t) = At+(1/2)Bt^2 + C then plug in v(0) to solve for C

Answer 2

Then take the next integral and plug X(0)

Answer 3

yerp

Answer 4

i take the integral of the first integral? and then plug in x(0)?

Answer 5

yep

Answer 6

note you need to solve for c first

Answer 7

how did you get (1/2)bt^2 ?

Answer 8

anti derivative

Answer 9

the integral of Bt

Answer 10

A*0+(1/2)B*0^2 + C = vo

c = v0

Answer 11

ohhhhhh. okay okay. i get it now @zzr0ck3r

Answer 12

great...

note: Newton was a p i m p

Answer 13

\[V(0) = V_{i} \] according to the boundary condition
So \[V(0) =\frac{ B0^{2} }{ 2 } + a(0) + C\]
\[ V(0) = C\]

\[ V(0) = vi\]
So \[ Vi = C\]
Plug \[ V(i)\]
into the orginal \[V(t)\] function as C