$A$ truck starting from rest moves with an acceleration of $5 \, m/s^2$ for $1 \, s$ and then moves with constant velocity. The velocity $w.r.t$ ground $v/s$ time graph for the block in the truck is (Assume that the block does not fall off the truck and the coefficient of friction $\mu = 0.2$):

$A$ balloon of total mass $M$ and a fixed size starts coming down with an acceleration $f$ $(f < g)$. The fraction of the total mass of the balloon which must be dropped from it so that it starts going up with an acceleration of $f$ (assuming negligible air resistance) is

$A$ rough inclined plane $BCE$ of height $\left(\frac{25}{6}\right) \text{ m}$ is kept on a rectangular wooden block $ABCD$ of height $10 \text{ m}$,as shown in the figure. $A$ small block is allowed to slide down from the top $E$ of the inclined plane. The coefficient of kinetic friction between the block and the inclined plane is $\frac{1}{8}$ and the angle of inclination of the inclined plane is $\sin^{-1}(0.6)$. If the small block finally reaches the ground at a point $F$,then $DF$ will be (Acceleration due to gravity,$g=10 \text{ ms}^{-2}$)

Two carts of masses $200 \, kg$ and $300 \, kg$ on horizontal rails are pushed apart. Suppose the coefficient of friction between the carts and the rails is the same. If the $200 \, kg$ cart travels a distance of $36 \, m$ and stops,then the distance travelled by the cart weighing $300 \, kg$ is ........ $m$.

Match Column-$I$ with Column-$II$ correctly.

Column-$I$	Column-$II$
$(1)$ Static friction	$(a)$ Limiting friction
$(2)$ Rolling friction	$(b)$ Ball bearing
	$(c)$ Object moving on a road

$A$ car of mass $500\, kg$ is driven with acceleration $1\, m/s^2$ along a straight level road against a constant external resistance of $1000\, N$. When the velocity is $5\, m/s$,the rate at which the engine is working is .............. $kW$.