Question $27$

$0\mathrm{.}5$ pts

With only a few exceptions, up until now we have considered constant forces and as a consequence constant accelerations. Here we will consider a particle under the influence of a position$-$dependent net force. Such a particle has an instantaneous acceleration determined by its instantaneous position. For particles under the influence of position$-$dependent forces, the work$-$energy theorem is useful because it can be used to determine changes in their speed.

A particle of mass $m$ experiences a one$-$dimensional, position$-$dependent force vec$(F)=F_x$hat$(x)$ for which $F_x(x)=\frac{F_0}{x_0}x+F_0$ with $x_0$ and $F_0$ both positive quantities with appropriate dimensions.

Assuming the particle experiences no other forces and is released from rest at $x=0,$ will the particle move toward the positive or negative $x-$direction?

Positive

Negative

Neither; it will remain at rest