contestada

The only force acting on a 2.0 kg body as it moves along a positive x axis has an x component Fx = −6 x N, with x in meters. The velocity at x = 3.0 m is 8.0 m/s. (a) What is the velocity of the body at x = 4.0 m? (b) At what positive value of x will the body have a velocity of 5.0 m/s?

Respuesta :

Answer:a-0

b-2 m

Explanation:

Given mass of the body is 2 kg

Force acting on the body =-6x N

Velocity at x=3m is 8m/s

Now acceleration of the body is -3x

a=-3x

[tex]\frac{vdv}{dx}[/tex]=-3x

vdv=-3xdx

integrating both sides we get

[tex]\int vdv=\int -3xdx[/tex]

[tex]\frac{v^2}{2}[/tex]=[tex]\frac{x^2}{2}[/tex]+c

Now at x=3m v=8m/s

substituting values

c=[tex]\frac{37}{2}[/tex]

Thus [tex]v^2=-3x^2+37[/tex]

Velocity will be zero after [tex]x=\sqrt{\frac{37}{3}}[/tex]

thus velocity of the body is zero at x=4 m

[tex]\left ( b\right )[/tex]

v=5m/s

25=-3x^2+37

x=2 m

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