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>#