$A$ force applied by an engine of a train of mass $2.05 \times 10^6 \; kg$ changes its velocity from $5 \; m/s$ to $25 \; m/s$ in $5$ minutes. The power of the engine is ........... $MW$.

$A$ motor pump lifts $6$ tonnes of water from a well of depth $25 \ m$ to the first floor of height $35 \ m$ from the ground floor in $20$ minutes. The power of the pump (in $kW$) is: $[g=10 \ ms^{-2}]$

An automobile engine of mass $m$ provides constant power $P$. The acceleration is given by $a = \frac{P}{mv}$. (Assume friction is absent). What is the distance covered by the vehicle while its velocity increases from $V_1$ to $V_2$?

$A$ car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to

$A$ bead of mass $400 \ g$ is moving along a straight line under a force that delivers a constant power $1.2 \ W$ to the bead. If the bead is initially at rest,the speed it attains after $6 \ s$ in $m \ s^{-1}$ is:

$A$ body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function of time is given by