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# M2) Calculus in kinematics help!!

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1. 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

THanks!
2. (Original post by liemluji)
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

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.
3. (Original post by RDKGames)
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 ?
4. (Original post by liemluji)
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 ?
Yes. Best to simply integrate everything that you're given then put a +c at the end. Then equate this to the given velocity and plug in t=0. With whatever is left standing, rearrange for c. Doing this you would find that c=2i-3j. From there on in do the same to get the position vector.

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