A particle traces the path vector r = (t^3, t+3, t^2 -4t) where t represents time; it flies off on a tangent when t=1 and then moves in a straight line with constant speed. Find its position when t=4.

Question

Do I just plug the 4 into the t's in vector r?

Answer 1

IT seems to me that the vector r is only valid to time=1, after that the particle is on a "tangent" at constant speed.

So find the position and velocity of the particle at time=1, then the velocity is constant for the next three seconds, find the new position. That is what I read into the problem.