First slide

Power

Question

Statement A : An engine A can perform a given work in 1 hr and engine B can perform the same work in ½ hr then B has greater power than A.
Statement B : Power is the dot product of force and velocity

Easy

A

A & B is correct
B

A & B are wrong
C

A is correct and B is wrong
D

A is wrong & B is correct

Solution

Average power = Total work done/Total time,
so average power of B is greater than that of A. Also,
$\large \Delta W=\vec F.\Delta \vec x$

$\large \therefore \frac {\Delta W}{\Delta t}=\vec F.\frac {\Delta \vec x}{\Delta t}$

$\large \therefore P = \mathop {\lim }\limits_{\Delta x \to 0} \frac{{\Delta W}}{{\Delta t}} = \vec F \left( {\mathop {\lim }\limits_{\Delta x \to 0} \frac{{\vec {\Delta x} }}{{\Delta t}}} \right) = \vec F .\frac{{d\vec x }}{{d\vec t }} = \vec {F.} \vec V$

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