# particle position and acceleration

#### mr.burger

##### New member
A particle moves along a straight line so that its position at any time t>0 seconds is given by s=t+(1/t). Find the position and the acceleration of the particle when it comes to rest.

#### tkhunny

##### Moderator
Staff member
You have s(t), giving position.

Find v(t), giving velocity, but finding the derivative, s'(t).

Find t0, such that v(t0) = 0.

Calculate s(t0) to answer one part.

Find the acceleration function, a(t), by finding the derivative of v(t).

Calculate a(t0) to answer the other part.

#### mr.burger

##### New member
that is all very confusing i need some better clarification and to be walked through better no offense i just have a hard time learning the way you showed it soroban does it really well

#### tkhunny

##### Moderator
Staff member
Did you read the clear examples in your book? A clear example here will NOT be any better.

If you follow the path the book shows, you may find it a little different from the one I showed. Either way, YOU will have to do it so you can SEE it and FEEL it and THINK about it. Calculus (and mathematics in general) is NOT a game that requires only the memorization of rules. You should be learning how to think.

My views. I welcome others'.

#### ChaoticLlama

##### Junior Member
Yes I agree, it seems that you, mrburger just looked at the exam review sheet and posted every question without trying them.

Anyway, for the particle question.

the function you are given, s(t) is the position of the particle at any time t.

finding the derivative of s(t) will produce v(t) the velocity at any time t.

Finding the derivative of v(t) will produce a(t) the acceleration at any time t.

s(t) = t + (1/t)

s'(t) = v(t) = 1 + -1/t²

v'(t) = a(t) = 2/t³

try it from there