Solve Parametric Particle Homework: Find Time, Speed at (3,1)

[turdferguson]

Homework Statement

Consider a particle along a curve C and whose position is given by the vector:
s(t) = < sqrt(t²), t³ - 3t >

Last part of the question:
There is an unknown force that is keeping this particle on trajectory C. At what value of t must the force cease in order for the particle to pass through the point (3,1)?
When will it arrive at this point and with what speed?

The Attempt at a Solution

Ive tried setting the slope of (3,1) and the point (xt, yt) to equal dy/dx. But I keep getting a value of t that places the point (3,1) on the tangent line behind the particles path. The particle reaches (3,1) at a time before it even gets to (xt, yt) on the curve.

t³-3t-3 / abs(t)-1 = (3t² -3)t/abs(t)

Is there anything wrong with the setup? Why do I keep getting an extraneous solution when letting t be >0 and when letting t be <0?

 

[turdferguson]

Nevermind, I got it. This thread can be deleted