A particle moves with a velocity of $(5\hat{\mathrm{i}}-3\hat{\mathrm{j}}+6\hat{\mathrm{k}})$m/s under the influence of a constant force $\overrightarrow{F}=(10\hat{\mathrm{i}}+10\hat{\mathrm{j}}+20\hat{\mathrm{k}})$ N. The instantaneous power applied to the particle is:

1. 200 J/sec

2. 40 J/sec

3. 140 J/sec

4. 170 J/sec

An automobile of mass m accelerates from rest, while the engine supplies constant power P. The speed of the automobile as a function of time is given by:

1.  $\mathrm{v} = {\left(\frac{2\mathrm{Pt}}{\mathrm{m}}\right)}^{1/2}$

2.  $\mathrm{v} = {\left(2\mathrm{Ptm}\right)}^{1/3}$

3.  $\mathrm{v} = {\left(\frac{8}{9}\frac{\mathrm{P}}{\mathrm{m}}{\mathrm{t}}^3\right)}^{1/2}$

4.  $\mathrm{v} = {\left(2{\mathrm{Pt}}^3\mathrm{m}\right)}^{1/2}$

A pump ejects 12,000 kg of water at a speed of 4 m/s in 40 s. The average rate at which the pump is working is:

1.  0.24 kW

2.  2.4 W

3.  2.4 kW

4.  24 W

An engine pumps liquid of density d continuously through a pipe of cross-sectional area A. If the speed with which liquid passes through the pipe is v, then the rate at which kinetic energy is being imparted to the liquid by the pump is:

1.  ${\mathrm{Adv}}^2$

2.  $\frac{1}{2}{\mathrm{Adv}}^2$

3.  $\frac{1}{2}{\mathrm{Adv}}^3$

4.  $\frac{1}{2}\mathrm{Adv}$

1.  8.1 kW

2.  10.2 kW

3.  12.3 kW

4.  7.0 kW

A water pump rated 400 W has an efficiency of 75%. If it is employed to raise water to a height of 40 m, then the volume of water drawn in 10 min is:-

1. 10.9 ${\mathrm{m}}^3$

2. 0.45 ${\mathrm{m}}^3$

3. 1.8 ${\mathrm{m}}^3$

4. 0.25 ${\mathrm{m}}^3$

A truck of mass 30,000 kg moves up an inclined plane of slope 1 in 100 at a speed of 30 km/h. The power of the truck is: (given g=10 ms^-2):

1. 25 kW

2. 10 kW

3. 5 kW

4. 2.5 kW

The power supplied to a particle of mass 2 kg varies with time as $\mathrm{P}=\frac{3{\mathrm{t}}^2}{2}$ Watt, where t is in seconds. If the velocity of a particle at t = 0 is v = 0, then the velocity of the particle at t = 2 s will be:

1. 1 m/s

2. 4 m/s

3. 2 m/s

4. $2\sqrt{2}$ m/s

A particle of mass m is moving in a circular path with a speed v = kt, where k is constant and t is time. The instantaneous power delivered to the particle is:

1.  Zero

2.  mkt

3.  ${\mathrm{mk}}^2\mathrm{t}$

4.  ${\mathrm{mk}}^2{\mathrm{t}}^2$

The speed of a particle moving in a circular path decreases with time. The instantaneous power due to the force acting on it will be:

1.  Positive

2.  Negative

3.  Zero

4.  Maybe positive or negative