need some more help

[mindshift]

i have a few more questions if you dont mind:

when t>0, a particle moves in a line defined by the function s=t+(1/t) . find the position and acceleration of the particle when it comes to rest.

ill probably have some more in a bit.

 

[soroban]

Hello, mindshift!

Simple rules to remember:

s(t) is the position of the particle.

The first derivative, s'(t), is the velocity of the particle: v(t)

The second derivative, s"(t) or v'(t), is the acceleration of the particle, a(t).

when t>0, a particle moves in a line defined by the function s = t + (1/t)
Find the position and acceleration of the particle when it comes to rest.

The particle is at rest when its velocity is zero.

. . We have: . v(t) .= .s'(t) .= .1 - t^-2 .= .0

. . . Multiply through by t²: . t² - 1 .= .0 . . ---> . . t = ±1

. . . We are told that t > 0, so t = 1 is the only solution.

At t = 1, its position is: . s(1) .= .1 + 1/1 .= .2


The acceleration is: . a(t) .= .v'(t) .= .2t^-3 .= .2/t³

At t = 1, its acceleration is: . a(1) .= .2/1³ .= .2