The challenge of the more accurate method you describe is balancing how much CPU is used to find the point in game time where a collision occurs because it is almost certainly at some point between your tick times. You have to perform the calculation at many units of time across the tick delta with the significance level you care about, with more calculations necessary as velocities of bodies increases.

Of course, this is what physics engines do, and why you should probably use one instead of reinventing the wheel.

In terms of showing how a game loop and really basic game physics works, however, this is a pretty clean and understandable example.