The velocity and acceleration of particle give position vector

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The position vector of the particle is defined as s = e^(-2t)i + sin(2t)j + 5tk. The velocity is calculated by differentiating the position vector with respect to time, resulting in a velocity of -2i + 2j at t=0. To find the acceleration, the velocity vector is differentiated again, initially yielding an incorrect result. The correct acceleration, after properly differentiating all components, is determined to be 4i + 10k. This highlights the importance of careful differentiation in vector calculus.
jake241190
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the position vector of the particle is given by

s=e^-2ti+sin(2t)j+5t^k

calculate its velocity and acceleration at t=0
to get the velocity i differentiated with respect to t and substituted in t=0, giving me

velocity=-2i+2j and that's the same as the answer given but I am not sure how to get the acceleration i tried differentiating again and got a answer
acceleration= 4i+0i+0k and this isn't correct
 
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never mind i know what I've don i forgot to differentite the k bit the second time giving
acceleration= 4i+10k
 

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