A block of mass 2 kg initially at rest moves under the influence of a time-dependent force F -4 t - The power developed by the force at t - 2 seconds isA- 16 WB- 30 WC- 32 WD- 48 W

Given, F = 4t î From Newton's 2^nd law of motion, for a constant mass nbsp; F = ma ⇒a nbsp; = nbsp; Fm ∴a = nbsp; 4t2 î = 2t m/s^2î v = ∫^t_0 a dt = ...

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Standard XII

Physics

Power, Force and Velocity

A block of ma...

Question

A block of mass $2 kg$ initially at rest moves under the influence of a time-dependent force $\to F = 4 t^i .$ The power developed by the force at $t = 2 seconds$ is

16 W

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32 W

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48 W

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30 W

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Solution

The correct option is B $32 W$
Given, $\to F = 4 t^i$

From Newton's $2^{n d}$ law of motion, for a constant mass
$\to F = m \to a$
$\Rightarrow \to a = \frac{\to F}{m}$

$∴ \to a = \frac{4 t}{2}^i = 2 t^i$

$v = \int_{0}^{t} a d t = 2 \int_{0}^{t} t d t = t^{2} \Rightarrow \to v = t^{2}^i$

we know that, $P = \to F . \to v = (4 t^i) . (t^{2}^i) = 4 t^{3} W$

At, $t = 2 seconds, P = 4 (2)^{3} = 32 W$

Hence option B is the correct answer

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A block of mass 2 kg initially at rest moves under the influence of a time-dependent force →F=4t ^i. The power developed by the force at t=2 seconds is

The correct option is B 32 WGiven, →F =4t ^i From Newton's 2nd law of motion, for a constant mass →F=m→a ⇒→a=→Fm ∴→a=4t2 ^i=2t ^i v=∫t0 a dt=2∫t0t dt=t2⇒→v=t2^i we know that, P=→F.→v=(4t ^i).(t2 ^i)=4t3 W At, t=2 seconds,P=4(2)3=32 W Hence option B is the correct answer

A block of mass $2 kg$ initially at rest moves under the influence of a time-dependent force $\to F = 4 t^i .$ The power developed by the force at $t = 2 seconds$ is