A particle moves along the x axis. Its position is given by the equation x=2+3t-(t^2) with x in meters and t in seconds. Determine
(a) its position at the instant it changes direction and
(b) its velocity when it returns to the position it had at t = 0.

Question

A particle moves along the x axis. Its position is given by the equation x=2+3t-(t^2) with x in meters and t in seconds. Determine
(a) its position at the instant it changes direction and
(b) its velocity when it returns to the position it had at t = 0.

parthkohli · Answer

First of all, when this thing changes its direction, it would have the velocity zero.  What is the velocity of this particle?  Differentiate to find out!$$x' = 3 - 2t$$Which is clearly zero at $t = 3/2~\rm sec$.

Plug the value of $t$ in the position function and there you have it.

parthkohli · Answer

For the second one, you have to first know the position it has at $t =0$.  The position is $x_0=2$. 

So now, you've got to know the other value of $t$ for which $x=2$.  Can you do that?