### Problem StatementThe position vector of a particle is given by:\[ \mathbf{r} = 15t\mathbf{i} + 1.2t^2\mathbf{j} - 1.2(t^3 - 3)\mathbf{k} \]where \( t \) is the time in seconds from the start of the motion, and where \( \mathbf{r} \) is expressed in meters. For the condition when \( t = 4 \) seconds, determine the power \( P \) developed by the force:\[ \mathbf{F} = 31\mathbf{i} - 37\mathbf{j} - 24\mathbf{k} \, \text{N} \]which acts on the particle.### SolutionFirst, we need to find the velocity \( \mathbf{v}(t) \) of the particle by differentiating the position vector \( \mathbf{r}(t) \) with respect to time \( t \):\[ \mathbf{v}(t) = \frac{d\mathbf{r}}{dt} \]Given \( \mathbf{r}(t) \):\[ \mathbf{r} = 15t\mathbf{i} + 1.2t^2\mathbf{j} - 1.2(t^3 - 3)\mathbf{k} \]Differentiating each component with respect to \( t \):\[ \frac{d}{dt} (15t) = 15 \]\[ \frac{d}{dt} (1.2t^2) = 2.4t \]\[ \frac{d}{dt} (-1.2(t^3 - 3)) = -3.6t^2 \]Therefore:\[ \mathbf{v}(t) = 15\mathbf{i} + 2.4t\mathbf{j} - 3.6t^2\mathbf{k} \]Next, we evaluate \( \mathbf{v}(t) \) at \( t = 4 \) seconds:\[ \mathbf{v}(4) = 15\mathbf{i} + 2.4 \times 4 \mathbf{j} - 3.6 \times 4^2 \mathbf{k} \]\[ \mathbf{v}(4) = 15\mathbf{i} + 9.6\

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The position vector of a particle is given by r = 15ti + 1.2t²j - 1.2(t³ – 3)k, where t is the time in seconds from the start of the motion and where r is expressed in meters. For the condition when t = 4 s, determine the power P developed by the force F = 31i - 37j - 24k N which acts on the particle. Answer: P = i kW

The position vector of a particle is given by r = 15ti + 1.2t²j - 1.2(t³ – 3)k, where t is the time in seconds from the start of the motion and where r is expressed in meters. For the condition when t = 4 s, determine the power P developed by the force F = 31i - 37j - 24k N which acts on the particle. Answer: P = i kW

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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