First slide

Power

Question

A body of mass 1 kg begins to move under the action of a dependent force $\large \vec F = (2t\hat i+3t^2\hat j)$ N $\large \hat i\;and \;\hat j$ are unit vectors along x and y axis. What power will be developed by the force in the time t?

Moderate

A

(2t² + 3t³)W
B

(2t² + 4t⁴)W
C

(2t³ + 3t⁴)W
D

(2t³+ 3t⁵)W

Solution

$\large Given\;that\\ \overrightarrow F = (2t\hat i + 3{t^2}\hat j) = \overrightarrow a = \frac{{\overrightarrow F }}{m} = 2t\hat i + 3{t^2}\hat j \\ Hence\;,\;\overrightarrow V = \int\limits_0^t {\overrightarrow a \;\;dt = {t^2}\hat i} + {t^3}\hat j \\ \therefore P = \overrightarrow F .\overrightarrow V = 2t.{t^2} + 3{t^2}.{t^3} = (2{t^3} + 3{t^5})w \\$

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