When is a particle speeding up or slowing down?

[Alain12345]

I need help with a question asking if the particle is speeding up or slowing down.

A particle moves on a vericle line. It's position, s, in metres at t seconds is given by s(t)= t^3-9t^2+24t

a) determine the velocity and acceleration functions
I got v(t)= 3t^2-18t+24 and a(t)= 6t-18

b) When is the particle moving up? Down?
I got when 0<t<2, t>4 and it's slowing down at 2<t<4

c) When is the particle speeding up? Slowing down?

I thought that I have to use a similar method to part b and make an interval chart, but I don't think I'm doing it right. I used the a(t) function and found the zero and used that in the chart.


Can someone help me out? Thanks.

 

[Office_Shredder]

It's speeding up whenever the acceleration and velocity are either both negative, or both positive. This is because then the acceleration and velocity are both in the same direction. When the acceleration is negative, and velocity positive, or vice versa, the particle is slowing down.

Also, in part b, you write it's slowing down for 2<t<4, when it should say "moving down". You might want to make sure you didn't write that down on your answer sheet too :p