Question

Find the speed of a particle with the given position function: r(t) = ti + 5t^2j + 3t^6k.

A. |v(t)| = 1 + 100t^2 + 324t^10

Answer 1

The speed of a particle with a given position function can be found by taking the magnitude of its velocity vector.

Step-by-step explanation:

The speed of a particle can be found using the magnitude of its velocity vector. In this case, the velocity vector v(t) is equal to the derivative of the position vector r(t). The velocity vector can be found by taking the derivative of r(t) with respect to time:

v(t) = dr(t)/dt = i + 10tj + 18t^5k

The speed of the particle can be found by taking the magnitude of the velocity vector:

|v(t)| = √(1^2 + (10t)^2 + (18t^5)^2) = √(1 + 100t^2 + 324t^10)