While it may appear as possible duplicate The difference between "follow" using についていく、「あと?」をつける、「あと?」をついていく , the specificity here is a school/training context which was not discussed previously
Is the current use in the sentences (to be able to keep with the studies) an extension of the original meaning (to follow) ?
And what is the difference between 付いてくる and 付いていく ? (If there is)
The first sentence describes a group of friends that help children thar dropped out:
課題のボランティア活動にはいくつか選択肢があり、学校の通常の授業についていけない小学生(多くは不登校児童だ)を集めたアフタースクールの手伝いをするというのも、そのひとつだった
Second sentence: if you cannot keep up, you'll be punished !
ついてこられなかったらお仕置きだからね