You want to look into what's called Special Relativity. There are many, many books on this (it's an Einstein thing, so is always popular). It's really not that hard to understand either.
And in answer to your question: time dilation as it's called only starts being noticed when you get close to the speed of light, which is about 300,000,000 metres/second. So even 1000mph is pretty slow compared, so maybe it'll work out to be a difference of a second or after every several thousand years. Nothing much really at those speeds.