Greetings Michelle, I hope to help you, since I think I got it.
When I saw your images, i said to me, “ok, it looks like fragments with some rays highlights from the background” but later I read your comment telling that those are clips flying towards the viewer.
The thing is, this is called “Track Motion”
check the image below:

you need to have several clips, in several video tracks, then, you can arrange them into groups or in just 1 group (because you can have the option to do some parent motion*)
*parent motion: (I suggest you to check tutorials on youtube)
this is when you arrange a group of clips “below” the main video track, and you can move them all individually or collectively.
Maybe this is tricky for you to understand but to know best, the best way is doing some practice.
I have used this effect but not in that way (moving towards the viewer) but moving in a circular fashion, check it here:
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When I was working on my video, I found an incredible tool that Mr. Rofrano offers via vasst’s website:
https://vasst.com/store/sony-vegas-plug-ins/scattershot-3d-1.aspx
I found this reading this Thread:
https://forums.creativecow.net/thread/24/961407
I hope to help you, sorry for my long answer, but I am still obsessed with this track motion thing and I hope to see the guys around here, I have learned so much from them, they ROCK!!
Sorry for my bad english, kindest regards from Dominican Republic.
J. Baez.