The position vector of a particle moving in a plane is given by . Find the velocity.

Question

The position vector of a particle moving in a plane is given by  . Find the velocity.

Quizplus · Accepted Answer

The velocity is the derivative of the position vector with respect to time. Taking the derivative of the given position vector, we get:

v(t) = \i + 2t\j + 3t^2\k

Therefore, the velocity vector is <1, 2t, 3t^2>.

Since we are not given the value of t, we cannot determine the exact velocity vector. However, we know that the magnitude of the velocity vector is increasing with time because the coefficients of t^2 are positive.

Looking at the answer choices, we can see that option C has coefficients of 1, 2t, and 3t^2 in the i, j, and k directions, respectively, which matches our velocity vector. Therefore, the correct answer is C.

The Position Vector of a Particle Moving in a Plane