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Average and Instaneous Power

A constant po...

Question

A constant power P is applied on a particle of mass m. Find kinetic energy, velocity and displacement of particle as function of time t.

K = P t, v = \sqrt{\frac{P t}{m}}, S = \sqrt{\frac{6 P}{9 m}} t^{3 / 2}

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K = P t, v = \sqrt{\frac{P t}{m}}, S = \sqrt{\frac{8 P}{7 m}} t^{3 / 2}

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K = P t, v = \sqrt{\frac{2 P t}{m}}, S = \sqrt{\frac{8 P}{7 m}} t^{3 / 2}

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K = P t, v = \sqrt{\frac{2 P t}{m}}, S = \sqrt{\frac{8 P}{9 m}} t^{3 / 2}

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Solution

The correct option is D $K = P t, v = \sqrt{\frac{2 P t}{m}}, S = \sqrt{\frac{8 P}{9 m}} t^{3 / 2}$
Power supplied to particle= $\frac{d W}{d t} = P$
where $W$ is the work done on the particle.
This work done goes into the kinetic energy of the particle.
$⟹ \frac{d K}{d t} = P$
$⟹ K = P t$
$⟹ \frac{1}{2} m v^{2} = P t$
$⟹ v = \sqrt{\frac{2 P t}{m}}$
$⟹ \frac{d S}{d t} = \sqrt{\frac{2 P t}{m}}$
$⟹ \int_{0}^{S} d S = \int_{0}^{t} \sqrt{\frac{2 P}{m}} t^{1 / 2}$
$⟹ S = \sqrt{\frac{8 P}{9 m}} t^{3 / 2}$

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E_{c e l l} = 0.092 V w h e n \frac{[M^{2 +} + (a q)]}{[M^{4 +} (a q)]} = 10^{x}

G i v e n : E_{M^{4 +} / M^{2 +}}^{\circ} = 0.151 V; 2.303 \frac{R T}{F} = 0.059 V

P t (s) | H_{2} (g, 1 b a r) | H^{+} (a q, 1 M) | | M^{4 +} (a q), M^{2 +} (a q) | P t (s) E_{c e l l} = 0.092 V w h e n \frac{[M^{2 +} (a q)]}{[M^{4 +} (a q)]} = 10^{x} G i v e n : E_{M^{4 +} / M^{2 +}}^{0} = 0.151 V; 2.303 \frac{R T}{F} = 0.059 V

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Write the Nernst equation and emf of the following cells at 298 K:

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(ii) Fe(s) | Fe²⁺(0.001M) || H⁺(1M)|H₂(g)(1bar) | Pt(s)

(iii) Sn(s) | Sn²⁺(0.050 M) || H⁺(0.020 M) | H₂(g) (1 bar) | Pt(s)

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P t (s) | H_{2} (g, 1 b a r) | H^{+} (a q, 1 M) | | M^{4 +} (a q), M^{2 +} (a q) | P t (s)

E_{c e l l} = 0.092 V w h e n \frac{[M^{2 +} + (a q)]}{[M^{4 +} (a q)]} = 10^{x}

G i v e n : E_{M^{4 +} / M^{2 +}}^{\circ} = 0.151 V; 2.303 \frac{R T}{F} = 0.059 V

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