$A$ toy of mass $20 \,g$ at rest acquires a velocity $(3 \hat{i}-2 \hat{j}) \,m/s$ in $2 \,s$. The power of the toy is: (in $\,W$)

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is $1.5 \; m$,what is the speed (in $m/s$) with which the bob arrives at the lowermost point,given that it dissipated $5 \%$ of its initial energy against air resistance?

Two bodies $A$ and $B$ of mass $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. $A$ third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision,it is found that the instantaneous velocities of $A$ and $B$ are the same and the compression of the spring is $x_0$. The spring constant $k$ will be

$A$ body of mass $500 \ g$ is falling from rest from a height of $3.2 \ m$ from the ground. If the body reaches the ground with a velocity of $6 \ ms^{-1}$, then the energy lost by the body due to air resistance is (Acceleration due to gravity $= 10 \ ms^{-2}$) (in $J$)

An object of mass $M$ is at rest on a smooth horizontal surface. Objects of different masses collide head-on elastically with the object of mass $M$. All colliding objects have the same fixed kinetic energy $E$,and in each case,mass $M$ is initially at rest. The kinetic energy transferred to the stationary mass $M$ depends on the linear momentum $P$ of the incoming colliding mass. How does the energy transferred to $M$ vary with the linear momentum $P$?

The rate of doing work by a force acting on a particle moving along the $x$-axis depends on the position $x$ of the particle and is equal to $2x$. The velocity of the particle is given by the expression: