$A$ car of mass $m$ is driven with acceleration $a$ along a straight level road against a constant external resistive force $R$. When the velocity of the car is $V$,the rate at which the engine of the car is doing work will be

$A$ man of mass $50 \ kg$ carries an object to a height of $20 \ m$ in a time of $10 \ s$. The power used by the man in this process is $2000 \ W$. Find the mass of the object carried by the man (take $g = 10 \ m/s^2$). (in $kg$)

$A$ particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest,the force on the particle at time $t$ is:

$A$ body of mass $2\, kg$ is driven by an engine delivering a constant power $1\, J/s$. The body starts from rest and moves in a straight line. After $9$ seconds,the body has moved a distance (in $m$):

$A$ body of mass $1\, kg$ begins to move under the action of a time-dependent force $\overrightarrow{F} = (2t\hat{i} + 3t^2\hat{j})\, N$,where $\hat{i}$ and $\hat{j}$ are unit vectors along the $x$ and $y$ axes. What power will be developed by the force at time $t$?

Two bodies of mass $m_1$ and $m_2$ $(m_2 > m_1)$ are connected by a light inextensible string which passes through a smooth fixed pulley. The instantaneous power delivered by an external agent to pull $m_1$ with constant velocity $v$ is