A particle moves along a horizontal line so that its position at time t, t ≥ 0, is given by s(t) = 40 + te^−t/20.
Find the minimum velocity of the particle for 0 ≤ t ≤ 100.

The minimum velocity of the particle  = units

Step-by-step explanation:

Given - A particle moves along a horizontal line so that its position at time t,

t ≥ 0, is given by  s(t) = 40 + te^−t/20.

To find - Find the minimum velocity of the particle for 0 ≤ t ≤ 100.

Proof -

Velocity, v(t)  =

Now,

=  

                       = 0 +

                       =

⇒v(t) =

Now,

For minimum velocity, Put

Now,

           =

Now,

Put , we get

⇒t = 40

Now,

Check that the point is minimum or maximum

Calculate  

Now,

=

            =

⇒  =  > 0

∴ we get

t = 40 is point of minimum

So,

The minimum velocity be

v(40) =

      =

      =

⇒v(40) = units

∴ we get

The minimum velocity of the particle  = units

step-by-step explanation:

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