Question

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

• A. be independent of $\beta$
• B. drop to zero when $\alpha = \beta $
• C. go on decreasing with time
• D. go on increasing with time

Answer 1

Answer: (D)

$x = ae^{-\alpha t}+be^{\beta t}$
$\frac{dx}{dt} = -a \alpha e^{-\alpha t}+b \beta e^{\beta t}$
$v = -a \alpha e^{-\alpha t}+b \beta e^{\beta t}$
For certain value of $t$, velocity will increases.