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Particle moving with acceleration as below form \mathrm{A_0=\cos \theta+i \sin \theta}, where i is complex number. What's the displacement of the given particle -

Option: 1

\mathrm{(\cos \theta+i \sin \theta)}


Option: 2

\mathrm{(\sin \theta-i \cos \theta)}


Option: 3

\mathrm{(\cos \theta-i \sin \theta)}


Option: 4

\mathrm{-(\cos \theta+i \sin \theta)}


Answers (1)

best_answer

\mathrm{\text { Acceleration }\left(A_0\right)=\cos \theta+i \sin \theta}

Now, integrate it to get velocity - 

\mathrm{\text { Velocity }(V)=\int A_0 d \theta}

\mathrm{\text { Velocity }(k)=\int(\cos \theta+i \sin \theta) d \theta}

                           \mathrm{=(\sin \theta-i \cos \theta)\, \, \, \, -(1)}

Again integrate it to get displacement- 

\mathrm{\text { Displacement }(s)=\int v d \theta}

                                   \mathrm{\begin{aligned} & =\int(\sin \theta-i \cos \theta) d \theta \\ & =-\cos \theta-i \sin \theta \\ & =-(\cos \theta+i \sin \theta) \text { Ans } \end{aligned}}

Posted by

Pankaj

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