At any instant of time \(t\), the displacement of any particle is given by \(2t-1\) (SI unit) under the influence of force of \(5~\text N\). The value of instantaneous power is (in SI unit):
1. \(5\)
2. \(7\)
3. \(6\)
4. \(10\)
Subtopic:  Power |
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A particle moves with a velocity \((5\hat i-3\hat j+6\hat k)\) ms–1 horizontally under the action of constant force \((10\hat i+10\hat j+20\hat k)\) N. The instantaneous power supplied to the particle is:
1. \(200\) W
2. zero
3. \(100\) W
4. \(140\) W
Subtopic:  Power |
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The energy that will be ideally radiated by a \(100\) kW transmitter in \(1\) hour is:
1. \(1\times 10^{5}\) J
2. \(36\times 10^{7}\) J
3. \(36\times 10^{4}\) J
4. \(36\times 10^{5}\) J
Subtopic:  Power |
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An electric lift with a maximum load of \(2000\) kg (lift+passengers) is moving up with a constant speed of \(1.5\) ms–1. The frictional force opposing the motion is \(3000\) N. The minimum power delivered by the motor to the lift in watts is: 
(Take \(g=10\) ms–2)
1. \(23500\)
2. \(23000\)
3. \(20000\)
4. \(34500\)
Subtopic:  Power |
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Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? g=10 m/s2

1. 12.3 kW  2. 7.0 kW 
3. 10.2 kW  4. 8.1 kW
Subtopic:  Power |
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A body of mass \(1\) kg begins to move under the action of a time-dependent force \(\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) \) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along the \(\mathrm{X}\) and \(\mathrm{Y}\)-axis. What power will be developed by the force at the time (\(t\))?
1. \(\left(2 t^2+4 t^4\right) \) W
2. \(\left(2 t^3+3 t^3\right) \) W
3. \(\left(2 t^3+3 t^5\right)\) W
4. \(\left(2 t^3+3 t^4\right) \) W
Subtopic:  Power |
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A particle of mass \(m\) is driven by a machine that delivers a constant power of \(k\) watts. If the particle starts from rest, the force on the particle at time \(t\) is:
1. \( \sqrt{\frac{m k}{2}} t^{-1 / 2} \)
2. \( \sqrt{m k} t^{-1 / 2} \)
3. \( \sqrt{2 m k} t^{-1 / 2} \)
4. \( \frac{1}{2} \sqrt{m k} t^{-1 / 2}\)

Subtopic:  Power |
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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:
1.  \(t^{\frac{1}{2}}\)
2.  \(t^{\frac{-1}{2}}\)
3. \(\frac{t}{\sqrt{m}}\)
4. \(t^2 P_0\)

Subtopic:  Power |
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An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 ms-1. The mass per unit length of water in the pipe is 100 kg m-1.What is the power of the engine?

1. 400 W

2. 200 W

3. 100 W

4. 800 W

Subtopic:  Power |
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A particle of mass \(M\) starting from rest undergoes uniform acceleration. If the speed acquired in time \(T\) is \(V\), the power delivered to the particle is:
1. \(\frac{1}{2}\frac{MV^2}{T^2}\)
2. \(\frac{MV^2}{T^2}\)
3. \(\frac{1}{2}\frac{MV^2}{T}\)
4. \(\frac{MV^2}{T}\)

Subtopic:  Power |
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