It is less vivid; "raced after" emits a feeling of either action, suspense, or energy. It allows the reader to connect and fully understand what is going on. "ran after" is vague and emits little high energy.
I went to go makeup the work I missed from the other day
In an admirably purposeful, determined, and unwavering manner
Answer:
The detail, "And someone gave little Davy Hutchinson a few pebbles", contributes to the text because his mother was the one being stoned, but the person who gave him some pebbles was suggesting that he needed to start participating at a young age, just as everyone else did.