# Math Help - Postion and Velocity Function

1. ## Position Functions

Never mind... I figured it all out!

2. Originally Posted by LRoseT
A particle moves along the x- axis where t>0 and it's position is given by
x(t)= (t*ln(t))-t

a). What is the velocity function?
b). When is the particle moving left? (Be careful of the domain of the position function!)
c). At t=2, is the particle speeding up or slowing down?

I need the answers to all three PLEASE.
a)
$v = \frac{dx}{dt} = ln(t)$

b) The particle will be moving left when v > 0. So when is this?

c) To answer speeding up or slowing down you need to look at the acceleration. Have a care: look at the magnitude of the velocity when you take your derivative because the question is not asking if the velocity is increasing/decreasing, it is asking about the speed.

-Dan