(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given that the acceleration vector is

a(t) = (-16cos(-4t))i+ (-16sin(-4t))j+ -2tk,

the initial velocity is v(0) = i + k

and the initial position vector is r(0) = i + j + k, compute:

The velocity vector v(t) = ___i + ____j + ____k

The position vector r(t) = ___i + ____j + ____k

2. Relevant equations

v(t) = r'(t) = ∫a(t)dt

3. The attempt at a solution

v(t) = ∫a(t)dt = ∫a(t) = (-16cos(-4t))i+ (-16sin(-4t))j+ -2tkdt

v(t) = 4sin(-4t)i+ (-4cos(-4t)j+ (-t^2)k

r(t) = ∫v(t) = ∫4sin(-4t)i+ (-4cos(-4t))j+ (-t^2)kdt

r(t) = -cos(-4t)i+ sin(-4t)j+ (-1/3)t^3k

I've double checked my integration but can't figure out what I did wrong. None of the parts of my answers are correct.

Thanks!

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# A(t), v(t), r(t) converting, integration and derivatives

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