how does its distance from the starting point increase as a function of time? It would be a horrible blunder to invoke the middle-school formula of distance equals rate times time because that formula is valid only when the rate—the car’s speed—is constant, which it certainly isn’t here. On the contrary, in this problem the car’s speed is ramping up at every instant. We are no longer in the sleepy world of constant speed. This is the thrilling world of constant acceleration.
I feel talked down to, because this "middle school blunder" is precisely where my head goes when faced with this type of problem.
