In pre-calculus last week my teacher explained a scenario in which a man throws a rock down a well and takes 4 seconds for you to hear the rock hit the bottom. How far downs the well? Last years I took regular physics and learned that distance equals Velocity x Time. So knowing that gravity pulls with 9.8m/s/s I assumed I would just multiply 4 by 9.8. Sadly I was wrong and my quick method of solving this problem was incorrect, we ended up using a very very large quadratic equation. My question Is why I was wrong in my answer?
When I think about the problem assume I went wrong by using 9.8 as if it were a regular velocity when in fact it is a constant acceleration, so the speed is constantly increasing. If that is the case then can anyone explain mathematically how quickly gravity accelerates in a 4 second period and also what the easiest and most efficient way of solving this problem would be to your knowledge?
Ps, this isn't homework I'm curious as to how this works