Question

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

Answer 1

The displacement of particle is given by

$x=a{e}^{-\alpha t}+b{e}^{\beta t}$

The velocity of particle,

$v=\frac{dx}{dt}=-\alpha a{e}^{-\alpha t}+b\beta e^{\beta t}$