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Equipartition Theorem

A particle is...

Question

A particle is released from rest at origin. It moves under influence of potential field $U = x^{2} - 3 x$ , kinetic energy at $x = 2$ is:

2 J

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1 J

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1.5 J

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0 J

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Solution

The correct option is A $2 J$
F=ma=- $\frac{d U}{d x}$
mv $\frac{d v}{d x}$ = $- 2 x + 3$
on integration
$m \frac{v^{2}}{2} = - x^{2} + 3 x$
$K E = 3 \times 2 - 2^{2} = 2 J$

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Similar questions

A particle is released from rest at origin. It moves under influence of potential field $U = x^{2} - 3 x$ , kinetic energy at $x = 2$ is:

U = x^{2} - 3 x

x = 2

U = x^{2} - 3 x

x = 2

U = 5 x^{2} - 20 x + 2 (J)

x

m

x = - 3 m

x

x = 1

U (x) = x^{2} - 10 x + 25

U

x

x = 3

4 J

x = 3

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