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

Gravels are dropped on a conveyor belt at the rate of $0.5 \, kg/s$. The extra force required in newtons to keep the belt moving at $2 \, m/s$ is

$A$ rocket lifts off from the ground and accelerates upwards at $1 \ m \ s^{-2}$. $20 \ s$ after liftoff,a piece breaks off from the bottom of the rocket. After breaking off,how much time does it take approximately to reach the ground (in $s$)? (Take $g = 10 \ m \ s^{-2}$)

An isolated rail car originally moving with speed $v_0$ on a straight,frictionless,level track contains a large amount of sand. $A$ release valve on the bottom of the car malfunctions,and sand begins to pour out straight down relative to the rail car. What happens to the speed of the rail car as the sand pours out?

$A$ balloon has a mass of $10\,g$ in air. The air escapes from the balloon at a uniform rate with a velocity of $4.5\,cm/s$. If the balloon shrinks completely in $5\,s$,then the average force acting on the balloon will be (in $dyne$).

In the first second of its flight,a rocket ejects $1/60$ of its mass with a velocity of $2400\,m/s$. The acceleration of the rocket is ............ $m/s^2$.