How to find the velocity and acceleration at t=0?

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Answer 1 · 2018-06-14T01:36:24

$vec v(0) = < 6, 2,-2>$
$vec a(0) = <0,4,4>$

We differentiate

$vec r(t) = <2sin 3t,e^{2t},1+e^{-2t}>$

component by component to calculate the velocity :

$vec v(t) = < d/dt(2sin 3t),d/dt(e^{2t}),d/dt(1+e^{-2t})>$
$qquad qquad = <6 cos 3t,2e^{2t},-2e^{-2t}>$

Differentiating once again, we get the acceleration:

$vec a(t) = < d/dt(6 cos 3t),d/dt(2e^{2t}),d/dt(-2e^{-2t})>$
$qquad qquad = <-18 sin 3t,4e^{2t},4e^{-2t}>$

Thus, at $t=0$ we have

$vec v(0) = < 6, 2,-2>$
$vec a(0) = <0,4,4>$