The displacement x of a particle varies with time t as x = ae-α t+beβ t where a, b, α and β are positive constants. The velocity of the particle will

Question

The displacement x of a particle varies with time t as x = ae-α t+beβ t where a, b, α and β are positive constants. The velocity of the particle will (A) be independent of β (B) drop to zero when α = β  (C) go on decreasing with time (D) go on increasing with time

Tardigrade Admin · Accepted Answer

x = ae-α t+beβ t (dx/dt) = -a α e-α t+b β eβ t v = -a α e-α t+b β eβ t For certain value of t, velocity will increases.

Q. The displacement x of a particle varies with time t as $x = a e^{- α t} + b e^{βt}$ where $a, b, α$ and $β$ are positive constants. The velocity of the particle will

be independent of $β$

drop to zero when $α = β$

go on decreasing with time

go on increasing with time

$x = a e^{- α t} + b e^{βt}$
$\frac{d x}{d t} = - a α e^{- α t} + b β e^{βt}$
$v = - a α e^{- α t} + b β e^{βt}$
For certain value of $t$ , velocity will increases.

Q. The displacement x of a particle varies with time t as x=ae−αt+beβt where a,b,α and β are positive constants. The velocity of the particle will

be independent of β

drop to zero when α=β