Learn English – Meaning of warm vs hot when talking about weather

They are both correct.

I am a twenty-year-old student:

1. "20" and "year" are linked by the hyphen to create a single term ("20-year") that modifies "old."
2. "20-year" and "old" are linked by the hyphen to create a single term ("20-year-old") that modifies "student."

I am twenty years old:

1. "old" is a predicate adjective for "I." (as in "I am old.") As a single-word adjective for "I," it is not joined with a hyphen to the previous adjective, "years."
2. "years" modifies "old," and "20" modifies "year". "20" and "years" are not acting as a single adjective for "old," so they, too, do not need a hyphen.

The easy understanding:

If the adjective phrase serves as a single modifier before the noun (student, in the second sentence), it needs a hyphen (or hyphens, as in this case). Adjective phrases have no plural forms on the words forming them (the word year you asked). When you use a noun as an adjective (year-old), it must be singular. That's why there is no -s there.

If it is after the noun, it doesn't need a hyphen (or hyphens). When the same words (years) are used not as an single adjective, which means they modify the noun separately, the noun is plural. That's why there is an -s there (unless it's She is 1 year old).

Another example:

• The ceiling is ten feet high.
• The room has a ten-foot ceiling.

In physics, there are two types of energy potential and kinetic.

Potential energy is just that, something that has the possibility of happening. An apple hanging from a tree, a book on a table.

Once the apple or book falls from their perch, the potential energy is transformed into kinetic energy, it is realised as movement with possibly secondary vibrations or ripples which can be felt.

In your excerpt

He was kinetic and yet totally in control.

The author is using her vocabulary of movement to describe the appearance of Prince on stage, the energy he exuded, his movements, and his dancing. She is saying he was moving quickly and energetically, but was still in control. If you've ever seen Prince perform, you will know that he is always in control.

Also with performers, they can be described as being kinetic at an energetic level. Electric might be a good synonym where the performer takes on a buzzing/humming quality with their presence, like a high voltage transformer.

Ballistic would imply a singular, sudden unidirectional movement.
Bouncing off the walls would imply movement without intent.

Neither would be appropriate for describing how Prince moves and performs.