A force 2-3-k- N acting on a body- displaces it from r1-2-3k- m to r2-8t2-9t3-7tk- m- Find the instantaneous power delivered by the force at t-1 sec-

Displacement vector is given by S=r_2 r_1 =(8t^2î+9t^3ĵ+7tk̂) (2î+ĵ+3k̂) =(8t^2 2)î+(9t^3 1)ĵ+(7t 3)k̂ m Work done by the force F is given by W=F.S =(2î+3ĵ+k̂). ...

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Byju's Answer

Standard XII

Physics

Average and Instaneous Power

A force 2î+3ĵ...

Question

A force $(2^i + 3^j +^k) N$ acting on a body, displaces it from $_{1} = (2^i +^j + 3^k) m$ to $_{2} = (8 t^{2}^i + 9 t^{3}^j + 7 t^k) m$ . Find the instantaneous power delivered by the force at $t = 1 sec$ .

100 W

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60 W

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80 W

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120 W

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Solution

The correct option is D $120 W$
Displacement vector is given by $\to S =_{2} -_{1}$
$= (8 t^{2}^i + 9 t^{3}^j + 7 t^k) - (2^i +^j + 3^k)$
$= (8 t^{2} - 2)^i + (9 t^{3} - 1)^j + (7 t - 3)^k m$
Work done by the force $\to F$ is given by
$W = \to F . \to S$
$= (2^i + 3^j +^k) . [(8 t^{2} - 2)^i + (9 t^{3} - 1)^j + (7 t - 3)^k)]$
$= (16 t^{2} - 4) + (27 t^{3} - 3) + (7 t - 3)$
$W = (27 t^{3} + 16 t^{2} + 7 t - 10) J$

Instantaneous power is given by, $P = \frac{d W}{d t}$
$\Rightarrow P = \frac{d}{d t} (27 t^{3} + 16 t^{2} + 7 t - 10) = 81 t^{2} + 32 t + 7$

$∴$ Instantaneous power at $t = 1 sec$ is given by $P_{t = 1 sec} = 81 \times (1)^{2} + 32 \times (1) + 7$
$= 81 + 32 + 7$
$= 120 W$

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Average and Instaneous Power

Standard XII Physics

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A force (2^i+3^j+^k) N acting on a body, displaces it from →r1=(2^i+^j+3^k) m to →r2=(8t2^i+9t3^j+7t^k) m. Find the instantaneous power delivered by the force at t=1 sec.

A force $(2^i + 3^j +^k) N$ acting on a body, displaces it from $_{1} = (2^i +^j + 3^k) m$ to $_{2} = (8 t^{2}^i + 9 t^{3}^j + 7 t^k) m$ . Find the instantaneous power delivered by the force at $t = 1 sec$ .