Two bodies $A$ and $B$ of masses $1.5 \ kg$ and $3 \ kg$ are moving with velocities $20 \ m \ s^{-1}$ and $15 \ m \ s^{-1}$ respectively. If the same retarding force is applied on the two bodies,then the ratio of the distances travelled by the bodies $A$ and $B$ before they come to rest is

Two identical balls $A$ and $B$ are released from the positions shown in the figure. They collide elastically on the horizontal portion $MN$. All surfaces are smooth. The ratio of the maximum heights attained by $A$ and $B$ after the collision will be (Neglect energy loss at $M$ and $N$):

$A$ man of mass $80 \ kg$ goes to the market on a scooter of mass $100 \ kg$ with a certain speed. On application of brakes,the stopping distance is $S_1$. The man returns home on the same scooter,with the same speed with a $60 \ kg$ bag of rice. If $S_2$ is the new stopping distance when the brakes are applied with the same force,then:

The position $x$ of a particle moving along the $x$-axis at time $t$ is given by the equation $t = \sqrt{x} + 2$,where $x$ is in metres and $t$ is in seconds. The work done by the force in the first $4 \ s$ is .............. $J$.

The displacement $x$ of a particle moving in one dimension under the action of a constant force is related to the time $t$ by the equation $t = \sqrt{x} + 3$,where $x$ is in meters and $t$ is in seconds. The work done by the force in the first $6$ seconds is.....$J$

$A$ constant force $\vec{F} = 3\hat{i} - 2\hat{j} - \hat{k} \text{ N}$ causes a displacement $\vec{r} = 2\hat{i} - 3\hat{j} - 3\hat{k} \text{ m}$ in $2 \text{ s}$. The work done and the power are respectively: