A particle moves along the x axis in such a way that it's position at a time is given by: 3t^4-16t^3+24t^2 -55.... How do I find at what time(s) does the particle change direction? I have already found the acceleration and velocity of the particle and at what values of t it is at rest, and the velocity when the acceleration is first zero

Question

A particle moves along the x axis in such a way that it's position at a time is given by: 3t^4-16t^3+24t^2    -5<t>5.... How do I find at what time(s) does the particle change direction? I have already found the acceleration and velocity of the particle and at what values of t it is at rest, and the velocity when the acceleration is first zero

paxpolaris · Answer

change in direction is when x(t) has a relative max. or min.

paxpolaris · Answer

so you need to find all t where:

$\large velocity = 0$, and 

$\large acceleration \ne 0$