Velocity to position, acceleration and angular momentum vectors from v=5t² i + 3/t j – t k

[itr]

Homework Statement

Velocity vector for a .5kg body, t=1s to t=35s, is v=5t^2 i + 3/t j – t k

WHat is the position vector? what is the angular momentum vector?what is the acceleration vector? what is torque exerted on the body?

Homework Equations

L=rxp=rxmv
T=rxf=rxma

The Attempt at a Solution

Position vector: 5/3t^3 i + 1/3ln(t) j - 2t^-2 k
Acceleration Vector: 10t i + (t-3)/t^2 j - k
I am not good in cross product so i might need verification if i did it write...granted that my vectors above are right...
L=rxp=rxmv
L=((t/6lnt)-3/2))i, ((-15/6)-(5/6t^2))j, ((5/t^6)-(5/6t^2 lnt))k.

I won't write out torque vector because it takes awhile and if i know how do do what is above right, i can manage the torque one...so please somebody review my work

 

[itr]

All it is is checking my work...becasue there are further parts that run off of this work and i want to make sure i got this part right

 

[itr]

bold letteres are vectors

 

[itr]

PLEASE somebody check this out for me...just not sure about the derivatives/integrals and the cross product exectution

 

[ehild]

Neither the position vector nor the acceleration is correct. Look after the rules of derivation and integration.

ehild