Find the position vector of a particle whose acceleration vector is a = (1, 2) with an initial velocity vector (0, 0) and initial position vector (1, 0). (10 points)

Question

Please give explanation and show work. Thank you so much!

Answer 1

a = <1,2>

v = <t+c1,2t+c2>
v(0) = <0,0> so c1=c2=0
v = <t,2t>

r = <1/2 t^2+c1, t^2+c2>
r(0) = <1,0> so c1=1, c2=0
t = <1/2 t^2+1, t^2>

Answer 2

is that the answer or do we have to plug in numbers from there?