InterviewSolution
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InterviewSolution
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A particle moves with an initial `v_(0)` and retardation alphav, where v is its velocity at any time t. (i) The particle will cover a total distance `v_(0)/alpha`. (ii) The particle will come to rest after time `1/alpha`. (iii) The particle will continue to move for a very long time. (iv) The velocity of the particle will become `v_(0)/2` after time `(1n2)/alpha`A. (i), (ii)B. (ii), (iii)C. (i), (ii), (iv)D. All |
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Answer» Correct Answer - C `(dv)/(dt)=-alpha v` `int_(v_(0))^(v)(dv)/v=-alphaint_(0)^(t) dt` `| log_(e)v|_(0)^(v)=-alpha|t|_(0)^(t)` `log_(e)v-log_(e)v_(0)=-alpha t` `log_(e)(v//v_(0))=-alpha t` `v//v_(0)=e^(-alpha t)` Velocity in terms of t `v=v_(0)e^(-alphat) ...(i)` `(ds)/(dt)=v_(0)e^(-alphat)` `int_(0)^(s) ds=v_(0)int_(0)^(t) e^(-alphat)dt` `s=v_(0)|e^(-alphat)|_(0)^(t)/-alpha=v_(0)/-alpha(e^(-alphat)-e^(0))` `s=v_(0)/alpha(1-e^(-alphat)) ...(ii)` `v=0impliese^(-alphat)=0impliest=oo`, (iii) is O.K. At `t=oo, s=v_(0)/alpha,` (i) is O.K. `v=v_(0)e^(-alphat)impliesv_(0)/2=v_(0) e^(-alphat)` `e^(alphat)=2impliesalphat log_(e)e=log_(e)2` `t=(loge^(2))/alpha=(In 2)/alpha`, (iv) is O.K. |
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