SATHEE: Motion in a Plane - Result Question 12

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) $35 J / s$

(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

$P_{ins} = F \cdot \cos θ v = \vec{F} \cdot \vec{v}$

which is the scalar product of force and velocity vector.

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

Answer:

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Motion in a Plane - Result Question 12

14. A particle moves with a velocity v→=6i^−4j^+3k^m/s under the influence of a constant force F→=20i^+15j^−5k^N. The instantaneous power applied to the particle is

Answer:

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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