Is a particle with y-position -t² free along the y-direction?

[catstevens]

Homework Statement

From an inertial reference frame S, the vector position of a particle of mass
m1 = 1kg is given by r1(t)=(tx-hat - t^2y-hat)m.
The vector position of a particle m2=2m1 is given by r2=(t)=(tx-hat +t^3y-hat)m

Is particle #1 free along the y-direction? Explain

Homework Equations

If the particle is free along the y-direction then the y's would equal to 0.

The Attempt at a Solution

r1= -t^2y
r2=+t^3y
=not free?
(I am actually unsure if my definition of free is true)

 

[Fredrik]

"Free" means "unaffected by forces", or equivalently that the potential is constant. In this case, it means you have to check if it's accelerating in the y-direction or not.

 

[catstevens]

Particle #1's motion along the y-direction is -t^2.
Would this mean that it is not free?

 

[Fredrik]

That's its position at time t. What's its acceleration at time t?