A) go on decreasing with time
B) be independent of \[\alpha \] and \[\]
C) drop to zero when \[\alpha \] = \[\]
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, \[A=-a\alpha {{e}^{-\alpha t}},\] \[B=b\beta {{e}^{\beta t}}\] The value of term \[A=-\,a\alpha {{e}^{-\alpha t}}\] 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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