(B) The instantaneous power $P$ delivered by a force $\vec F$ to a particle moving with velocity $\vec v$ is given by the dot product of the force and

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(B) The instantaneous power $P$ delivered by a force $\vec F$ to a particle moving with velocity $\vec v$ is given by the dot product of the force and velocity vectors:$P = \vec F \cdot \vec v$Given $\vec F = 20\hat i + 15\hat j - 5\hat k \, N$ and $\vec v = 6\hat i - 4\hat j + 3\hat k \, m/s$.$P = (20\hat i + 15\hat j - 5\hat k) \cdot (6\hat i - 4\hat j + 3\hat k)$$P = (20 \times 6) + (15 \times -4) + (-5 \times 3)$$P = 120 - 60 - 15$$P = 120 - 75$$P = 45 \, J/s$.

Class 11 Physics Work, Energy, Power and Collision Power

Medium

$A$ particle moves with a velocity $\vec v = 6\hat i - 4\hat j + 3\hat k \, m/s$ under the influence of a constant force $\vec F = 20\hat i + 15\hat j - 5\hat k \, N$. The instantaneous power applied to the particle is ......... $J/s$.

A
$35$
B
$45$
C
$25$
D
$195$

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Work, Energy, Power and Collision

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Power

$A$ truck of mass $10,000 \ kg$ is moving up an inclined plane with a slope of $1 \ m$ in $50 \ m$. If the speed of the truck is $36 \ km/hr$,find the power of the engine in $kW$. (Take $g = 10 \ m/s^2$)

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An electric motor exerts a force of $40 N$ on a cable and pulls it by a distance of $30 m$ in one minute. The power supplied by the motor (in Watts) is

Easy

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$A$ $60 \ kg$ man runs up a staircase in $12 \ s$ while a $50 \ kg$ man runs up the same staircase in $11 \ s$. The ratio of the rate of doing their work is:

Medium

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Power of a water pump is $2 \, kW$. If $g = 10 \, m/s^2$,the amount of water it can raise in one minute to a height of $10 \, m$ is .............. $liter$.

MediumAIPMT 1990

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$A$ force applied by an engine on 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 (in $MW$)

DifficultTS EAMCET 2001

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$A$ particle moves with a velocity $\vec v = 6\hat i - 4\hat j + 3\hat k \, m/s$ under the influence of a constant force $\vec F = 20\hat i + 15\hat j - 5\hat k \, N$. The instantaneous power applied to the particle is ......... $J/s$.

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$A$ truck of mass $10,000 \ kg$ is moving up an inclined plane with a slope of $1 \ m$ in $50 \ m$. If the speed of the truck is $36 \ km/hr$,find the power of the engine in $kW$. (Take $g = 10 \ m/s^2$)

An electric motor exerts a force of $40 N$ on a cable and pulls it by a distance of $30 m$ in one minute. The power supplied by the motor (in Watts) is

$A$ $60 \ kg$ man runs up a staircase in $12 \ s$ while a $50 \ kg$ man runs up the same staircase in $11 \ s$. The ratio of the rate of doing their work is:

Power of a water pump is $2 \, kW$. If $g = 10 \, m/s^2$,the amount of water it can raise in one minute to a height of $10 \, m$ is .............. $liter$.

$A$ force applied by an engine on 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 (in $MW$)

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