   Chapter 13.4, Problem 19E

Chapter
Section
Textbook Problem

# The position function of a particle is given by r(t) = ⟨t2, 5t, t2 − 16t⟩. When is the speed a minimum?

To determine

To find: when the speed is a minimum.

Explanation

Given:

r(t)=t2,5t,t216t

Formula used:

Write the expression to find the velocity.

v(t)=r(t) (1)

Write the expression to find the speed.

speed=|v(t)| (2)

Substitute t2,5t,t216t for r(t) in equation (1),

v(t)=ddt(t2,5t,t216t)=ddt(t2),ddt(5t),ddt(t216t)=2t,5,2t16

Substitute 2t,5,2t16 for v(t),

Speed=|2t,5,2t16|=(2t)2+(5)2+(2t16)2=4t2+25+[

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