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

[physixguru]

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>>>

 

[Doc Al]

Show your solution and why you aren't satisfied with it.

 

[physixguru]

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 knowledge.