Time for an analysis.
0:08 Goku is sitting on the earth (representing that he is earth's hero.) It also demonstrates that child Goku is in fact an adult-turned child, this essentially tells the story and presents the problem
0:16 this scene is important as it showcases the story and demonstrates all of the characters personalities. Starting with Pan. We see Pan struggling to hold Giru/Gill (who I will call "robot" from here on out) Pan struggling to hold the robot symbolizes her internal struggle of how she wants control in her life and is tired of being treated like a child, at
0:18, Pan loses the robot then goes into a fit of rage, symbolizing her anger and bossy attitude and how she demands things to go her way.
0:16 Next we see Goku's personality, he's eating, which is a classic anime symbol for the lighthearted "simple but stupid" anime protagonist. If you look very closely at
0:17, you will see him make a slight glance at Pan, checking to see if she is okay, referencing their relationship. Goku later looks up at Giru and smiles realizing that everything is okay.
0:16 Lastly, Trunks. Trunks remains calm, cool and collected, during his appearance. Only to be distracted by Pan, implying that she will be a nuisance to him throughout the series (which she is) Trunks immediately gains his composure and returns to his calm self, smiling, giving the audience an "you're in for bumpy ride" glance.
0:21 to
0:39 aren't really anything important other than a funny glance of Mr.Satan giving the peace sign and the show giving the viewer a quick view of what is happening (It's a space ship, It's going to an alien planet and it is obviously an alien planet because it has dinosaurs (Creatceous), weird trees and a really close moon. It also shows the space ship crash land, Probably referring to How Pan left behind the little piece of the spaceship in ep 2, it also provides a bit of comedy.)
0:41 Next, we're introduce to naked Goku, This demonstrates how Goku embraces his youth and innocence (through nudity) and Pan angrily hands him clothes, showing her desire to become an adult and telling the audience that she won't put up with Goku's immaturity. Those laughing alien cats-things laugh, telling the audience that the show will have humorous elements to it.
0:49 More humorously/lighthearted elements. Telling the audience absolutely now that this series will be more lighthearted than DBZ
0:51 This bit seems to be for younger kids who have not seen DBZ. It seems to be used to tell the audience that the main characters have supernatural powers.
0:54-
1:00 Nothing really important. Just a shot of supporting characters. It seems to be looking out from the spaceship
1:01 Another scene that demonstrates the characters personalities and fighting styles. Goku does a punch symbolizing his Anime hero personality who is always rushing towards a fight. Pan opens her arms, demonstrated her youthfulness and her graceful fighting style. Trunks does a-sort-of salute, symbolizing his soldier-like attitude and the fact that he usually fights to kill/defeat like a soldier. The lyrics also make reference to Courage, Pride and Love. I'm guessing Goku represents Courage, Trunks represents Pride and Pan represents Love.
1:07-
1:16 It shows a scene of a battle (which fits in with the lyrics of exactly when the singer sings "fight") Next we see each of the characters demonstrating their abilities. We see Goku use his signature Kamehameha wave which also tells the audience that we will be seeing old elements from DBZ in the show and showcases Goku's abilities. We also see Tapion's (Future Trunks') sword In Trunk's hand which is a nod to DBZ elements that will make a return and it showcases Trunks abilities.
1:16 random shot of a planet
1:17 Next we cut to Pan who has no special ability so she just resorts to jumping on the bird/ostrich thing, demonstrating her ability to think outside the box. We see Goku and the spaceship (Obviously being piloted by trunks,) following behind her, symbolizing that they will always be there. This also gives the audience a hint that they are after the dragon balls.
1:27 Next we see the gang on Monmaasu, where they are resting. Pan picks up a flower and smells it, representing the beauty of nature. She is startled by a creature which then holds out a twig-like flower. This represents that along that way, they will meets enemies and problems but they will always still find good in their world along the way.
1:31 And one of the final scenes of the characters facing an omega shenron-lookalike monster together and easily winning with teamwork.
1:39 Pan and Trunks escape the area, but Goku breaks out, symbolizing his non-practically personality and his wildness.