$A$ $60 \ kg$ man runs up a staircase in $12 \ s$ while a $50 \ kg$ man runs up the same staircase in $11 \ s$. The ratio of the rate of doing their work 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 .............. $W$.

$A$ particle moves with a velocity $\vec{v} = 5\hat{i} - 3\hat{j} + 6\hat{k} \text{ m/s}$ under the influence of a constant force $\vec{F} = 10\hat{i} + 10\hat{j} + 20\hat{k} \text{ N}$. The instantaneous power will be ............... $\text{J/s}$.

$A$ force of $5 \,N$ acts on a body initially at rest. If the instantaneous power due to the force at the end of the third second $(t=3 \,s)$ is $5 \,W$, then the mass of the body is (in $\,kg$)

$A$ body of mass $m$ starts from rest and acquires a velocity $v$ in time $t$ under the action of a constant force $F$. The instantaneous power delivered to the body at time $t$ is:

$A$ vehicle of mass $m$ starts from rest and accelerates. If the engine delivers a constant power $p$,what is the velocity of the vehicle at time $t$?