Perception is for observation, Investigation is for deduction.
Some of this answer will be observations on how Wizards has done it so far and some of this will be logic, and some of it will be mechanics.
First for the headline question. It depends. when to use Investigation, and when to use Perception is not entirely clear yet, and I'm hoping we'll get more guidance in the DMG late this year. The guidance from the rules is that the two skills mostly seem to differ in the methods by which they are found.
Depending on the exercise, either, or both of the skills may be used.
For passive checks, you're almost always looking at Perception being the skill of record. While all skills can be used passively, some skills make more sense than others. Perception is the hallmark passive skill, whereas investigation makes less sense as a passive skill.
If the character is alert to the possibility of hidden objects/traps, but not actively searching, he's using passive perception.
The guidance for this seems to be (though we can't confirm yet), that the DC for actively looking for something is regularly about 5 less than the DC for passively looking for something (or sometimes actively looking always reveals it).
So here's how I would play it. Traps can be noticed with perception passively (usually DC 15). If the PC is looking, ask them how they are looking. If it's observational, then use Perception. If it's deductive, use Investigation. When they are searching for items, again, either skill is appropriate. This is somewhat counter to how WOTC has written adventures so far. They are always written to use perception to notice traps. Passive with a higher DC and active with a lower.
Investigation also has broader uses such as when you are trying to track clues, or put something together. It's also a great "roll for a hint" kind of skill if your PCs get stuck and need some help figuring out what to do next.
Tracking is mentioned only briefly, in/around the pages you mentioned, in both the PHB and the DMG. And as you pointed out, in the PHB and in the DMG it doesn't specify tracking as having any maximum speed.
On PHB page 181, under Travel Pace:
A fast pace makes characters less perceptive, while a slow pace makes it possible to sneak around and to search an area more carefully (see the "Activity While Traveling" section later in this chapter for more information).
This sentence, depending on how you read it, could mean that any "Activity While Traveling" (which is the section Tracking falls under) can only be taken while moving at a slow pace:
... a slow pace makes it possible to to search an area more carefully (see the "Activity While Traveling" section ...
However, several activities specify how they operate under different speeds, meaning this interpretation doesn't hold up.
Additionally, Foraging, another Activity While Traveling that points to full rules in the DMG, has the following statement (DMG page 111):
Characters can gather food and water as the party travels at a normal or slow pace.
It makes sense that Tracking would have a similar statement, but it does not, so for the time being there's no RAW restriction on tracking at a fast pace.
You can, however, interpret it as being RAI due to Foraging or due to the negative implication of the Barbarian ability.
Best Answer
There are no skill checks in D&D 5e
Don't feel bad if you missed it, the Player's Handbook sucks at explaining it.
There are Ability Checks in D&D 5e
The first question to ask is which ability score is the correct one for tracking and finding tracks?
Strength, Dexterity, Constitution and Charisma don't immediately suggest themselves, although I can see circumstances where they would - tracking someone through a crowd by reading disturbances and asking questions, could use Charisma for sure. Or Dexterity if you are tracking someone across rooftops perhaps?
You are generally left with:
Now, consider the task of tracking or finding tracks in the particular circumstances: is it primarily analytic, or primarily intuitive?
There is no correct answer and different circumstances can give one answer one time and the other answer another time.
You're the DM, you make the call.
Once you've decided on the ability; is there one or more applicable skills?
If the PC has a skill that is applicable then they can apply their proficiency bonus to the roll.
For tracking: is Survival applicable? Of course, it is.
Perception? Yes.
Insight? Definitely.
Arcana? If the thing being tracked is magical, why not?
Following a wild animal? Nature is applicable.
There are no off-limits skills. If your player can convince you why it should apply; be convinced.
At my table, my call is "Make an [ability] Ability Check?" and I expect and encourage "Can I apply [skill]?"
I highly recommend these "no skill" character sheets to emphasise this.