Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position.

Question

a(t) = 2 i + 6t j + 12t2 k, v(0) = i,
r(0) = 2 j − 7 k

Answer 1

a = 2i + 6tj + 12t^2k
v = 2ti + 3t^2j + 4t^3k + c
at t=0, v=i, so c = i and
v = (2t+1)i + 3t^2j + 4t^3k

r = (t^2+t)i + t^3j + t^4k + c
use r(0) to see that c = 2j-7k so
r = (t^2+t)i + (t^3+2)j + (t^4-7)k