position vector r(t) at time t, for particle traveling....

[cheffy]

A particle traveling in a straight line is located at the point (1, -1, 2) and has speed 2 at time t=0. The particle moves towards the point (3, 0, 3) with constant acceleration 2i+j+k. Find its position vector r(t) at time t.

Help! I integrated the acceleration function to a velocity function, but I don't know how to figure in the speed 2 to get the constants so I can integrate the velocity to position. Thank you!

 

[arthur ohlsten]

I believe this is what you want:
direction vector=[3-1]I + [0-(-1)]J+[3-2]K
direction vector=2I+J+K

acceleration vector = 2I+J+K
the vector consists of a magnitude and direction, or unit vector

acceleration magnitude = [4+1+1]^1/2
direction unit vector= [1/[6]^1/2][ [2I+J+K]

l acceleration l =6^1/2
l velocity l=6^1/2 t + C but at t=0 l velocity =2
2= c

l velocity l = 6^1/2 t + 2
l position l = 6^1/2t^2+2t+C
but at t=0 particle is at I-j+2k

POSITION AT ANY TIME IS
[I-J+2K]+[6^1/2 t^2+2t][1/6^1/2][2I+J+K] n answer
[I-J+2K]+[t^2+[1/3]sqrt6t][2I+J+K] answer

please check math for errors
Arthur