M2) Calculus in kinematics help!!

hi,

Just to make sure if I'm understanding this topic properly,

if the question is

for the following acceleration vectors, find the velocity vector v and the position vector r at time t consistent with the given initial condition

a=(4t-3)i + (6t-2)k, given that v=2i-3j and r=i+j+2k when t=0

is the answer v= (2t^2-3t+2)i -3tj + (3t^2-2t)k

r= (2/3 t^3 -3/2 t^2 +2t +1)i + (-3/2 t^2 +1)j + (t^3 -t^2 +2)k ?

what I was unsure about was if differentiating for eg 3I+2tj would just be 2j

If there's any mistakes please help me through

THanks!

Your j component of the velocity is incorrect (i and k are correct). You wouldn't get 0 if you differentiated that, and we KNOW it has to be 0 because we can see there is no j vector in our acceleration, hence it is 0j. As a result your position vector is wrong too.

would the j component be just -3j then? or is there no j component at all?
if the j component is 0, but in the question it says v=2i-3j when t=0, is there still no j component ?