An electric lift with a maximum load of $2000\,kg$ (lift + passengers) is moving up with a constant speed of $1.5\,m/s$. The frictional force opposing the motion is $3000\,N$. The minimum power delivered by the motor to the lift in watts is: $(g=10\,m/s^2)$

$A$ particle initially at rest is subjected to two forces. One is constant,the other is a retarding force proportional to the particle velocity. In the subsequent motion of the particle,

$A$ $100 \ kg$ gun fires a ball of $1 \ kg$ horizontally from a cliff of height $500 \ m$. It falls on the ground at a distance of $400 \ m$ from the bottom of the cliff. The recoil velocity of the gun is (Acceleration due to gravity $= 10 \ ms^{-2}$). (in $ms^{-1}$)

$A$ body of mass $3 \, kg$ hits a wall at an angle of $60^\circ$ with the wall and returns at the same angle. The speed of the body is $10 \, m/s$ and the impact time is $0.2 \, s$. Calculate the force exerted on the wall.

Can the work done by a frictional force be positive or negative?

The graph below shows the variation of a force $F$ with time $t$ on a body which is moving in a straight line. The dependence of force on time is $F \propto t^{n}$. Initially,the body is at rest. If the speed of the object is $2 \, m/s$ at $3 \, s$,then the speed at $4 \, s$ will be approximately (in $m/s$):