Question

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

a(t)= 56t i + sin(t) j + cos(2t) k
v(0)= i
r(0)= j

I need help finding r(t)

Thanks so much for your help!!

Answer 1

v(t) = 28t^2i - cos(t)j + 1/2 sin(2t)k + c
v(0)=0 so c = 1j
v(t) = 28t^2i + (1-cos(t))j + 1/2 sin(2t)k

r(t) = 28/3 t^3i + (t-sin(t))j - 1/4 cos(2t)k + c
r(0)=0 so c = 1/4 k
r(t) = 28/3 t^3i + (t-sin(t))j + 1/4 (1-cos(2t))k