i need a little help with this problem, i can get most of it set up but there is one part where i get stuck heres the question.(adsbygoogle = window.adsbygoogle || []).push({});

You are the captin of a spaceship that has been given the mission of flying from a spacestation at position (1,2,3) to a spacestation at position (4,7,5) in one hour, both departing and arriving with 0 velocity, and arriving with 0 acceleration. You are able to fire the engines so that the accereration of the spaceship is at time t (measured in hours after the departure) is given by the formula : a(t) = t^2b + tc +d for any choice of the constant vectors b,c and d. Determine choices of these constant vectors so that you can complete your mission.

so far this is what i have:

a(0)= d

a(1)= b+c+d = 0

v(t)= (1/3)*t^3*b + (1/2)*t^2*c +d*t +k_1

v(0)=0+k_1 so k_1=0

v(1)= (1/3)*b + (1/2)*c + d = 0

r(t)= (1/12)*t^4*b + (1/6)*t^3*c + (1/2)*t^2*d +k_2

r(0)= 0+ k_2 so k_2 = (1,2,3)

r(1)= (1/12)*b + (1/6)*c + (1/2)*d +(1,2,3) = (4,7,5)

i then tried to solve them in a linear system using t=1, since i have 3 variables and 3 equations, but im not sure how i would handle the r(1) situation since i have two points in the equation, and the rest are vectors.

can anyone help me out here?

thanks

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# Homework Help: Vector functions help

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