The position function of a particle is given by r(t) = <t^2, 9t, t^2 - 16t> When is the speed a minimum?

Question

The position function of a particle is given by
r(t) = <t^2, 9t, t^2 − 16t>

When is the speed a minimum?

Answer 1

I will set this up for you and you can take it from there.

 

You will have to find the velocity v from r, find speed v from the components of v, and then minimize v.

 

v = dr/dt = 2ti + 9j + (2t - 16)k

 

v = √[(2t)² + 9² + (2t - 16)²]

 

At a maximum or minimum,

 

dv/dt = 0

 

Find dv/dt, set it equal to 0, and solve for t.  You will have to perform a test to see if the value(s) of t give(s) a maximum or a minimum.