Chapter 12.3, Problem 52E

(a)

To determine

To calculate: The changes in the position, velocity, or acceleration of the particle when its position is given by the vector-valued function $r_2\left(t\right)=r_1\left(2t\right)$, where a particle is moving on the path $r_1\left(t\right)=x\left(t\right)i+y\left(t\right)j+z\left(t\right)k$.

(b)

To determine

To calculate: The changes in the position, velocity, or acceleration of the particle when its position is given by the vector-valued function $r_3\left(t\right)=r_1\left(\omega t\right)$, where a particle is moving on the path $r_1\left(t\right)=x\left(t\right)i+y\left(t\right)j+z\left(t\right)k$.