Particle Motion Help

[lgm123]

The function is p(t)=2t³-5t²-t+5.
a) Calculate when particle is at rest.
b) Calculate locations where particle is at rest.
c) Intervals where particle is moving forward and backward.
d) Total distance particle travels over 8 second interval.

The main problem I am having is that one of my time values I've calculated is negative and I don't know how to use it, or if I even need to use it at all.
If anyone can help, let me know!

Thanks!

 

[Romsek]

The function is p(t)=2t³-5t²-t+5.
a) Calculate when particle is at rest.
b) Calculate locations where particle is at rest.
c) Intervals where particle is moving forward and backward.
d) Total distance particle travels over 8 second interval.

The main problem I am having is that one of my time values I've calculated is negative and I don't know how to use it, or if I even need to use it at all.
If anyone can help, let me know!

Thanks!

negative time is perfectly valid. It just stands for time earlier than the moment you've happened to label 0.

Question (d) is poorly worded by the way. It asks you for the total distance over an 8 second interval but it doesn't specify which 8 second interval. To do this properly given the way they have worded it you would have to pick some t0 and find the distance the particle travels in the interval [t0, t0+8]. The parameter t0 would appear in the answer.

Note that finding the distance in [t0-8, t0] is just as valid, as is finding the distance in [t0-4, t0+4], and these will all result in different answers. The interval the distance is found over needs to be specified as part of the answer.

What they probably mean is find the total distance the particle moves between 0 and 8 seconds, i.e. t0=0.