## 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.

in progress
0

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

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