Motion in a Plane - Result Question 12
14. 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
(a) $45 J / s$
(b) $35 J / s$
(c) $25 J / s$
(d) $195 J / s$
[2000]
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Answer:
Correct Answer: 14. (a)
Solution:
- (a) As we know,
$ \begin{aligned} & P=\vec{F} \cdot \vec{v}=(6 \hat{i}-4 \hat{j}+3 \hat{k}) \cdot(20 \hat{i}+15 \hat{j}-5 \hat{k}) \\ & =6 \times 20-4 \times 15-3 \times 5=45 J / s \end{aligned} $
Instantanesous power can be calculated by
$P _{\text{ins }}=F \cdot \cos \theta v=\vec{F} \cdot \vec{v}$
which is the scalar product of force and velocity vector.
