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(D) The displacement is given by $x = a e^{-\alpha t} + b e^{\beta t}$.The velocity $v$ is the time derivative of displacement: $v = \frac{dx}{dt}$.$v

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go on increasing with time

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(D) The displacement is given by $x = a e^{-\alpha t} + b e^{\beta t}$.The velocity $v$ is the time derivative of displacement: $v = \frac{dx}{dt}$.$v = \frac{d}{dt}(a e^{-\alpha t} + b e^{\beta t}) = a(-\alpha) e^{-\alpha t} + b(\beta) e^{\beta t}$.$v = -a \alpha e^{-\alpha t} + b \beta e^{\beta t}$.As time $t$ increases,the term $e^{-\alpha t}$ decreases towards zero,while the term $e^{\beta t}$ increases exponentially. Since $b, \beta > 0$,the term $b \beta e^{\beta t}$ will dominate for large $t$,causing the velocity $v$ to increase with time.

The displacement $x$ of a particle varies with time $t$ as $x = a e^{-\alpha t} + b e^{\beta t}$,where $a, b, \alpha$,and $\beta$ are positive constants. The velocity of the particle will:

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