## 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 min

Question

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.

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3 days 2021-07-22T17:24:54+00:00 1 Answers 3 views 0

## Answers ( )

1. Answer:

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