A force - F -3 ti -5 - N acts on a body due to which its displacement varies as S -2 t 2-5 - m- Work done by this force in 2 s isA- 32 JB- 46 JC- 20 JD- 24 J

Given, S = 2t^2î 5ĵ ⇒v = dsdt = (4t)î Instantaneous power (P) = F. v= (3t î+5ĵ). (4tî)=12t^2 Work done, (W) = ∫^t_0 Pdt In 2 s, W = ∫^2_0 12t^2dt = [12t^33 ...

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Standard XII

Physics

Vector Addition

A force → F =...

Question

A force $\to F = (3 t^i + 5^j) N$ acts on a body due to which its displacement varies as $\to S = (2 t^{2}^i - 5^j) m$ . Work done by this force in $2 s$ is

32 J

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24 J

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46 J

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20 J

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Solution

The correct option is A $32 J$
Given, $\to S = 2 t^{2}^i - 5^j$
$\Rightarrow \to v = \frac{d \to s}{d t} = (4 t)^i$
Instantaneous power $(P) = \to F . \to v = (3 t^i + 5^j) . (4 t^i) = 12 t^{2}$
Work done, $(W) = \int_{0}^{t} P d t$
In 2 $s$ ,
$W = \int_{0}^{2} 12 t^{2} d t = \frac{12 t^{3}}{3} |_{0}^{2} = 4 t^{3} |_{0}^{2} = 4 (2)^{3} = 32 J$

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Similar questions

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A force →F=(3t^i+5^j) N acts on a body due to which its displacement varies as →S=(2t2^i−5^j) m. Work done by this force in 2 s is

The correct option is A 32 JGiven, →S=2t2^i−5^j ⇒→v=d→sdt=(4t)^i Instantaneous power (P)=→F.→v=(3t^i+5^j).(4t^i)=12t2 Work done, (W)=∫t0Pdt In 2 s, W=∫2012t2dt=12t33|20=4t3|20=4(2)3=32 J

A force $\to F = (3 t^i + 5^j) N$ acts on a body due to which its displacement varies as $\to S = (2 t^{2}^i - 5^j) m$ . Work done by this force in $2 s$ is