Find the velocity of a particle moving along the curve r(t) = (-8 + t³)i + 4t j - t² k at t = 1. A) 3i + 4j - 2k B) 6i - 2j C) 3i + 4j + 2k D) 0 E) 3i - 4j - 2k

Question

Quizplus · Accepted Answer

To find the velocity of a particle moving along the curve, we need to take the derivative of the curve with respect to time: r'(t) = 1³i + 4j - 1²k Substituting t = 1, we get: r'(1) = 3i + 4j - 2k Therefore, the velocity of the particle at t = 1 is 3i + 4j - 2k. Answer choice A is the only one that matches this result.

Find the Velocity of a Particle Moving Along the Curve