A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate ( dM ( t )/ dt )= bv 2( t ), where v ( t ) is its instantaneous velocity. The instantaneous acceleration of the satellite is:

Question

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate ( dM ( t )/ dt )= bv 2( t ), where v ( t ) is its instantaneous velocity. The instantaneous acceleration of the satellite is: (A) -(2 bv 3/ M ( t )) (B) -( bv 3/2 M ( t )) (C) -bv 3 (t) (D) -( bv 3/ M ( t ))

Tardigrade Admin · Accepted Answer

( dm ( t )/ dt )= bv 2 F text thast = v ( dm / dt ) Force on statellite =- vec v ( dm ( t )/ dt ) M(t) a=-v(b v2) a = a ( bv 3/ M ( t )) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/7f5c97e250ca2e788b92db889de627f2-.png" />

Q. A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{d M ( t )}{d t} = b v^{2} (t),$ where $v (t)$ is its instantaneous velocity. The instantaneous acceleration of the satellite is:

$- \frac{2 b v ^{3}}{M ( t )}$

$- \frac{b v ^{3}}{2 M ( t )}$

$- b v^{3} (t)$

$- \frac{b v ^{3}}{M ( t )}$

$\frac{d m ( t )}{d t} = b v^{2}$
$F_{thast} = v \frac{d m}{d t}$
Force on statellite $= - v \frac{d m ( t )}{d t}$
$M (t) a = - v (b v^{2})$
$a = a \frac{b v ^{3}}{M ( t )}$

Q. A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate dtdM(t)​=bv2(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is:

−M(t)2bv3​

−2M(t)bv3​

−bv3(t)

−M(t)bv3​