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  • Particle moving with velocity in the complex form with respect to time t is given by - <img alt="\mathrm{V_0=e^{i t}+\frac{e^{i t}}{2}}" src="https://entrancecorner.oncodecogs.com/gif.lat

Particle moving with velocity in the complex form with respect to time t is given by -

\mathrm{V_0=e^{i t}+\frac{e^{i t}}{2}}

what will be the acceleration (rate of velocity) at time t=3 sec

Option: 1

\mathrm{3 i e^{3 i}}


Option: 2

\mathrm{{\frac{1}{2} e^{3 i}}


Option: 3

\mathrm{\frac{i}{2} e^{3 i}}


Option: 4

\mathrm{\frac{3 i}{2} e^{3 i}}


Answers (1)

best_answer

Particle velocity is given by-

\mathrm{v_0=e^{i t}+\frac{e^{i t}}{2}}

Rate of velocity 

\mathrm{\begin{aligned} & =\frac{d v_0}{d t}=\frac{d}{d t}\left[e^{i t}+\frac{1}{2} e^{i t}\right] \\ & \frac{d v_0}{d t}=\frac{d}{d t} e^{i t}+\frac{1}{2} \frac{d}{d t} e^{i t} \\ & \frac{d v_0}{d t}=i e^{i t}+\frac{1}{2} i e^{i t} \\ & \frac{1 v_0}{1 t}=i e^{i t}+\frac{i}{2} e^{i t} \end{aligned}}

Rate of velocity (acceleration) 

\mathrm{\begin{aligned} & =i e^{3 i}+\frac{i}{2} e^{3 i} \\ & =i e^{3 i}\left[1+\frac{1}{2}\right] \\ & =i e^{3 i} \times \frac{3}{2} \\ & =\frac{3 i e^{3 i}}{2} \text { Ans. } \end{aligned}}

Posted by

Deependra Verma

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