This is a relatively simple problem, though it pestered me for a good while. I’m not even sure my answer is correct, but it certainly seems reasonable.
The idea is that acceleration is usually given in terms of velocity per time. Falling in gravity, you accelerate at a rate of 32 feet per second every second. And if you’re falling at a constant rate ‘a ft/s/s’, it’s easy enough to work out what your speed is at any time, and where you are at any time.
But suppose instead of feet/second/second, your acceleration was given in terms of feet/second/foot? That is, you’re slowing down based on how far you’ve gone instead of how long you’ve gone. So of course, the further you go, the slower you go, which means the longer it takes you to travel more distance, which means the slower you decelerate. But what does all this add up to?
So, we’ll say that you’re initially going at 100 m/s, decelerating at a rate of 10 m/s/m. Describe how position changes, velocity changes, and how are you actually decelerating in the traditional sense?
Here’s my solution, with no guarantee it is correct.
(more…)
