$A$ motor drives a body along a straight line with a constant force. The power $P$ developed by the motor must vary with time $t$ according to

Two particles,of masses $M$ and $2M$,moving as shown,with speeds of $10\, m/s$ and $5\, m/s$,collide elastically at the origin. After the collision,they move along the indicated directions with speeds $v_1$ and $v_2$ respectively. The values of $v_1$ and $v_2$ are nearly:

$A$ body of mass $2 \,kg$ is moving with a constant acceleration of $(2 \hat{i}+3 \hat{j}-\hat{k}) \,ms^{-2}$. If the displacement made by the body is $(3 \hat{i}-\hat{j}+2 \hat{k}) \,m$, then the work done is: (in $\,J$)

$A$ ball is released from the top of a tower. The ratio of work done by the force of gravity in the first,second,and third second of the motion of the ball is:

$A$ small disc of mass $m = 1 \,g$ slides down a smooth hill of height $h = 10 \,cm$ from rest and gets onto a plank of mass $M = 100 \,g$ as shown in the figure. Due to friction between the disc and the plank, the disc slows down and moves as one piece with the plank. The work done by the frictional force is approximately (Use $g = 10 \,m/s^2$): (in $\,J$)

$A$ small block of mass $200 \ g$ is placed on a horizontal slab at a height of $2 \ m$ above the floor. The block is pressed against a horizontal spring fixed at one end to compress the spring by $10.0 \ cm$. Upon releasing, the block moves horizontally until it leaves the spring. Calculate the horizontal distance covered by the block after leaving the slab and just before hitting the ground. The spring constant is $50 \ N \ m^{-1}$. (Assume $g = 10 \ m \ s^{-2}$) (in $m$)