I think what you should not do is using to acquiesce in sth. in passive voice. Use active voice:
Every student has asked himself this fundamental question at some key points in time, “What is my purpose ? What am I really supposed to be doing ?”. I know I did, especially when I acquiesced in something like listening to a boring lecture, or playing soccer.
Or if you want to put more emphasise on being forced to do something (and you respectfully and out of courtesy decided to accept the situation although you actually found it unpleasant or inappopriate):
Every student has asked himself this fundamental question at some key points in time, “What is my purpose ? What am I really supposed to be doing ?”. I know I did, especially when I was forced to acquiesce in something like listening to a boring lecture, or playing soccer.
This is grammatically correct. However, it has a problem with semantics: to acquiesc already carries an element of meaning saying "there is some force in play that makes me do things I do not actually want to do". Adding to be forced would be at least to some extent redundant. You can avoid this by simply saying:
Every student has asked himself this fundamental question at some key points in time, “What is my purpose ? What am I really supposed to be doing ?”. I know I did, especially when I was forced to something like listening to a boring lecture, or playing soccer.
Side topic:
Your combination of to acquiesc in sth. plus playing soccer has an (unwanted or wanted) comical effect. Basically you are saying
I acquiesc in running hectically around and chasing a ball
which contrasts the idea of you moving quickly and forcefully whith your supposed quiecy, as the verb to acquiesc of course is rooted in the Latin verb quiēscō (“repose, lie still”). So, acquiesc in running is a bit contradictive.