How to Calculate Velocity and Time in a Particle's Motion Along the x-Axis?

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A particle moving along the positive x-axis is influenced by a force proportional to the square of its position, with initial conditions of x=1m and velocity=0. The user calculated the velocity at x=0.5m by integrating the force over the displacement and applying the work-energy principle, but is unsatisfied with their solution. They seek guidance on determining the time it takes for the particle to reach 0.25m. The mass of the particle is 0.01 kg and the force constant is 0.01 N/m. The discussion emphasizes understanding the relationship between force, work, and motion to enhance knowledge in physics.
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A particle moves along positive x-axis.It is a acted upon by a force=k*1/2x^2 ,where x is the coordinate of particle in metre.At t=0 its x=1 and velocity=0.find::

1.The velocity at x=0.5m
2.Time at which particle reaches 0.25m

DID TRY A BIT..GOT THE ANSWER BUT AM NOT SATISFIED WITH MY SOLUTION.

THANKS A MILLION FOR ANY HELP>>>
 
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Show your solution and why you aren't satisfied with it.
 
i forgot to provide the mass>>>.01 kg
constant k=.01 n/m

i integrated the force over the displacement x= 1 to x=0.5
this gave me the work done..

now i know work done= change in k.e.
>>w = 1mv^2/2
i calculated velocity using this and got the answer..

i am confused how to proceed in the next part..

P.S: my ques are not homework ques.. ..i am solving these just to increase my knowlege.
 

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