$A$ particle of mass $0.2 \ kg$ is moving in one dimension under a force that delivers a constant power $0.5 \ W$ to the particle. If the initial speed of the particle is zero,the speed (in $m/s$) after $5 \ s$ is:

$A$ 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 ............... $\text{J/s}$.

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

$A$ body is moving uni-directionally under the influence of a source of constant power. Its displacement in time $t$ is proportional to

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 .............. $W$.

$A$ car of mass $m$ is driven with acceleration $a$ along a straight road against a constant external resistance $R$. When the velocity is $v$,the power of the engine is