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?