Question

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

• A. 200 J/s
• B. 40 J/s
• C. 140 J/s
• D. 170 J/s

Answer 1

Answer: (C)

$\vec{ v }=(5 \hat{ i }-3 \hat{ j }+6 \hat{ k }) m / s$
$\vec{ F }=(10 \hat{ i }+10 \hat{ j }+20 \hat{ k }) N$
$\therefore $ Power $\vec{ P }=\vec{ F } \cdot \vec{ v }$
$=(10 \hat{ i }+10 \hat{ j }+20 \hat{ k }) \cdot(5 \hat{ i }-3 \hat{ j }+6 \hat{ k })$
$=50-30 +120$
$=140\, J / s$