$A$ car of mass $1250 \ kg$ is moving with a velocity of $30 \ m/s$. If the engine delivers $30 \ kW$ of power and the resistive force acting on the car is $750 \ N$,find the maximum acceleration of the car.

$A$ motor boat is moving in a river with velocity $\vec{v} = 7 \hat{i} + 2 \hat{j} - 5 \hat{k} \text{ m/s}$. If the flow of water offers a resistive force $\vec{F} = 9 \hat{i} + 3 \hat{j} - 3 \hat{k} \text{ N}$, then the power of the boat is: (in $\text{ W}$)

An object of mass $m$ is projected with an initial velocity $u$ at an angle $\theta$ with the horizontal. What is the average power delivered by gravity in reaching the highest point?

$A$ body of mass $2 \,kg$ starts from rest and moves with uniform acceleration. It acquires a velocity $20 \,ms^{-1}$ in $4 \,s$. The power exerted on the body in $2 \,s$ in watts is

$A$ body of mass $4 \ kg$ is placed on a plane at a point $P$ having coordinates $(3, 4) \ m$. Under the action of force $\overrightarrow{F} = (2 \hat{i} + 3 \hat{j}) \ N$,it moves to a new point $Q$ having coordinates $(6, 10) \ m$ in $4 \ s$. The average power and instantaneous power at the end of $4 \ s$ are in the ratio of:

The average power generated by a $90 \ kg$ mountain climber who climbs a summit of height $600 \ m$ in $90 \ minutes$ is (Acceleration due to gravity $= 10 \ ms^{-2}$). (in $W$)