$A$ body of mass $m$ is initially at rest. It is subjected to a uniform acceleration such that it acquires a velocity $v$ in time $T$. The instantaneous power supplied to the body as a function of time $t$ is . . . . . . .

An elevator in a building can carry a maximum of $10$ persons,with the average mass of each person being $68 \; kg$. The mass of the elevator itself is $920 \; kg$ and it moves with a constant speed of $3 \; m/s$. The frictional force opposing the motion is $6000 \; N$. If the elevator is moving up with its full capacity,the power delivered by the motor to the elevator $\left(g = 10 \; m/s^{2}\right)$ must be at least .............. $W$.

The average power required to lift a $100 \ kg$ mass through a height of $50 \ m$ in approximately $50 \ s$ would be ............. $J/s$.

An electric motor produces a tension of $9000 \ N$ on a reel containing an electric cable at a rate of $2 \ ms^{-1}$. Calculate the power of the electric motor in $kW$.

$A$ man of mass $80 \ kg$ climbs a ladder of height $6 \ m$ in $10 \ s$. What is the average power generated by him in $HP$ (Horsepower)?

When a constant force is applied to a body moving with constant acceleration,power does not remain constant. For power to be constant,the force has to vary with speed as follows: