A particles moves in the xy-plane with position given by x(t)=5-2t and y(t)=t^2-3. In which direction is the particle moving as it passes through the point (3,-2)

Question

A particles moves in the xy-plane with position given by x(t)=5-2t and y(t)=t^2-3. In which direction is the particle moving as it passes through the point (3,-2)

Answer 1

To determine the direction in which the particle is moving at the point (3,-2), we first need to find the velocity vector at that point. The velocity vector is given by the derivative of the position vector:

v(t) = (x'(t), y'(t)) = (-2, 2t)

Now, plug in t=3 to find the velocity vector at the point (3,-2):

v(3) = (-2, 2(3)) = (-2, 6)

So, the velocity vector at the point (3,-2) is (-2, 6). This means that the particle is moving in the direction of the vector (-2, 6) as it passes through the point (3,-2).