A particle moves with a velocity of \(\left(5\hat{i}-3\hat{j}+6\hat{k}\right)\text{m/s}\) under the influence of a constant force \(\vec F = \left(10\hat{i}+10\hat j +20\hat k\right) \text{N} \). The instantaneous power applied to the particle is:
1. \(200~\text{J/s}\) 2. \(40~\text{J/s}\)
3. \(140~\text{J/s}\) 4. \(170~\text{J/s}\)
Subtopic:  Power |
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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, \(t\) is given by:
1. \(v=\left(\frac{2Pt}{m}\right)^{1/2}\)
2. \(v=\left(2Ptm\right)^{1/3}\)
3. \(v=\left(\frac{8Pt^3}{9m}\right)^{1/2}\)
4. \(v=\left(2Pt^3m\right)^{1/2}\)
Subtopic:  Power |
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A pump ejects \(12,000~\text{kg}\) of water at a speed of \(4~\text{m/s}\) in \(40~\text{s}\). The average rate at which the pump is working is:
1. \(0.24~\text{kW}\)
2. \(2.4~\text{W}\)
3. \(2.4~\text{kW}\)
4. \(24~\text{W}\)

Subtopic:  Power |
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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.  Adv2 2. 12Adv2
3. 12Adv3 4. 12Adv
Subtopic:  Power |
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Water falls from a height of \(60\) m at a rate of \(15\) kg/s to operate a turbine. The losses due to frictional forces are \(10\)% of energy. How much power is generated by the turbine? (\(g=10\) m/s2)
1. \(8.1\) kW
2. \(10.2\) kW
3. \(12.3\) kW
4. \(7.0\) kW
Subtopic:  Power |
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A water pump rated \(400~\text{W}\) has an efficiency of \(75\%\). If it is employed to raise water to a height of \(40~\text{m}\), then the volume of water drawn in \(10~\text{min}\) is:
1. \(10.9~\text{m}^{3}\)
2. \(0.45~\text{m}^{3}\)
3. \(1.8~\text{m}^{3}\)
4. \(0.25~\text{m}^{3}\)
Subtopic:  Power |
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A truck of mass \(30,000~\text{kg}\) moves up an inclined plane of slope \(1\) in \(100\) \(\left(\tan\theta = \frac{1}{100}\right)\) at a speed of \(30~\text{km/h}\). The power of the truck is: (given \(g=10~\text{ms}^{-2}\)):

1. \(25~\text{kW}\) 2. \(10~\text{kW}\)
3. \(5~\text{kW}\) 4. \(2.5~\text{kW}\)
Subtopic:  Power |
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The power supplied to a particle of mass 2 kg varies with time as P=3t22 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. \(1 \mathrm{~m} / \mathrm{s} \) 2. \(4 \mathrm{~m} / \mathrm{s} \)
3. \(2 \mathrm{~m} / \mathrm{s} \) 4. \(2 \sqrt{2} \mathrm{~m} / \mathrm{s}\)
Subtopic:  Power |
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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. mk2t 4. mk2t2

Subtopic:  Power |
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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

Subtopic:  Power |
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