The position function of a particle is given by $\mathbf { r } ( t ) = \left\langle 5 t ^ { 2 } , 5 t , 5 t ^ { 2 } - 100 t \right\rangle$ When is the speed a minimum?
A) $$t = 5$$
B) $t = 30$
C) $t = 20$
D) $t = 0$
E) $t = 10$

Question

Quizplus · Accepted Answer

The speed is minimized when the velocity is zero. The velocity is the derivative of the position function, so we have:$$\mathbf { v } ( t ) = \left\langle 10 t , 5 , 10 t - 100 \right\rangle$$Setting this equal to zero, we get:$$10 t = 0 \Rightarrow t = 0$$$$5 = 0 \Rightarrow \text{no solution}$$$$10 t - 100 = 0 \Rightarrow t = 10$$So the speed is minimized at $t = 0$ and $t = 10$.

The Position Function of a Particle Is Given By r(t)=⟨5t2,5t,5t2−100t⟩\mathbf { r } ( t ) = \left\langle 5 t ^ { 2 } , 5 t , 5 t ^ { 2 } - 100 t \right\rangler(t)=⟨5t2,5t,5t2−100t⟩

The Position Function of a Particle Is Given By $\mathbf { r } ( t ) = \left\langle 5 t ^ { 2 } , 5 t , 5 t ^ { 2 } - 100 t \right\rangle$