mechanics connected particles

on one question i was messed up by finding acceleration of ‘the car’ alone (as i was tricked by the question, boohoo) excluding the other particle, and i got it wrong because i was meant to take both particles as one. i figured its because i need tension in order to do it by itself? anyway, on another qiestion involving thrust, i did both the particles to be on the safe side but the markscheme told my ass that you can do it either way.. ??? i am tired and cant be bothered to crack another puzzle myself today. ill try and upload said questions.

Not really sure what you're asking? You've uploaded the questions, but not your attempts and you seem to know what your mistakes are?

i think my issue is the fact that, although i recognised that tension wouldnt allow me to find the acceleration of a single particle but when it comes to thrust, isnt that another unknown force that doesn’t let you find the acceleration using the lone particle? even though you somehow still get the same acceleration..