Level 2

A body starts from rest with uniform acceleration and acquires a velocity $V$ in time $T.$ The instantaneous kinetic energy of the body after any time $t$ is proportional to:

Two balls of the same mass are dropped from the same height onto the floor. The first ball bounces upwards from the floor elastically. The second ball sticks to the floor. The first applies an impulse to the floor of $I_1,$ the second applies an impulse $I_2$ (for the duration of collision). Then the relation between both the impulses is,

A body which is constrained for move along $Y$-direction is acted upon by a force $\overrightarrow{F}=\left(-2\hat{\mathrm{i}}+15\hat{\mathrm{j}}+6\hat{\mathrm{k}}\right) \mathrm{N}.$ The work done by this force in displacing the body by $10 \mathrm{m}$ along $Y$-axis is- 

An object is moving along a straight line path from $P$ to $Q$ under the action of a force $\overrightarrow{F}=\left(4\hat{\mathrm{i}}-3\hat{\mathrm{j}}+2\hat{\mathrm{k}}\right) \mathrm{N}$ If the co-ordinate of $P \& Q$ in metres are $\left(3, 2, -1\right) \& \left(2, -1, 4\right)$ respectively. Then the work done by the force is:

The potential energy of spring when stretched by a distance $x$ is $E.$ The energy of the spring when stretched by $x/2$ is -

A particle of mass $0.1 \mathrm{kg}$ is subjected to a force which varies with distance as shown in figure. If it starts its journey from rest at $x=0 \mathrm{m},$ its velocity at $x=12 \mathrm{m}$ is

A body of mass $m \mathrm{kg}$ initially at rest attains a velocity of $v \mathrm{m} {\sec }^{-1}$ in time $t$ under the action of a constant force $F$. The power supplied to the mass is-

In the figure shown, coefficient of restitution between $A$ and $B$ is $e=\frac{1}{2},$ then