A) go on decreasing with time
B) be independent of \[\alpha \] and \[\beta \]
C) drop to zero when \[\alpha =\beta \]
D) go on increasing with time
Correct Answer: D
Solution :
| Given, \[x=a{{e}^{-\alpha t}}+b{{e}^{\beta t}}\] |
| So, velocity \[v=\frac{dx}{dt}\] |
| \[=-a\alpha {{e}^{-\alpha t}}+b\beta {{e}^{\beta t}}\] |
| \[=A+B\] |
| where, \[A=-a\alpha {{e}^{-}},\,B=b\beta {{e}^{\beta t}}\] |
| The value of term \[A=-a\alpha {{e}^{-at}}\] decreases and of term \[B=b\beta {{e}^{\beta t}}\] increases with increase in time. As a result, velocity goes on increasing with time. |
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