simple motion Q thx~~~ (1 Viewer)

[Hikari Clover]

The acceleration a m/s<SUP>2 </SUP>of a particle P moving in a straight line is given by a=3(1-x<SUP>2</SUP>), where x metres is the displacement of the particle to the right of the origin. Initially the particle is at the particle and is at the origin and is moving with a velocity of 4m/s.
1.show that the velocity v m/s of the particle is given by v<SUP>2 </SUP>=16+6x-2x<SUP>3 </SUP>
<SUP> </SUP>2. will the particle ever return to the origin? Why?

the frist one is easy
for the second one,the answer on the back says "Yes", but i cant explain that , is the answer wrong?

 

[darryltolentino]

try graphing ur answer...but i think it will go back seeing the acceleration will be negative after x =1