For a particle showing motion under the force $F = -5(x - 2)^2$,the motion is .......

$A$ gas balloon is going up with a constant velocity of $10 \text{ m/s}$. When this balloon reached a height of $75 \text{ m}$,a stone is dropped from it and the balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is . . . . . . $\text{m}$. (Take $g = 10 \text{ m/s}^2$)

The equation of motion of a body is $\frac{dv}{dt} = -4v + 8$,where $v$ is the velocity in $m/s$ and $t$ is the time in seconds. The initial velocity of the particle was zero. Then,

Two stones are thrown up vertically and simultaneously but with different speeds. Which graph correctly represents the time variation of their relative position $\Delta x$? Assume that stones do not bounce after hitting the ground.

$A$ body of mass $0.40 \;kg$ moving initially with a constant speed of $10 \;m s^{-1}$ to the north is subject to a constant force of $8.0 \;N$ directed towards the south for $30 \;s$. Take the instant the force is applied to be $t=0$,the position of the body at that time to be $x=0$,and predict its position at $t=-5 \;s, 25 \;s, 100 \;s$.

Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X_{P}(t) = \alpha t + \beta t^{2}$ and $X_{Q}(t) = ft - t^{2}$. At what time,do both the buses have the same velocity?