I believe I heard at some point and time someone saying that it was possible to travel backwards in time by traveling at a certain speed. The following are my speculations on things and I might be false in a bunch of stuff, so please bare with me on that. I'm not really all that knowledgeable in this field. Here goes:
You cannot travel fast enough to go back in time because it takes time to get to where you are going. You may be able to prevent a future event by traveling at any speed to any location, but you cannot alter a past even by traveling at a speed.
Moving from one place, to another place takes a time, because if something goes from one place to another, it must have a measurement of speed and speed is measured with time as a variable. Speed is measured by distance/time. To have negative time in the speed calculation, you'd get a negative speed which is impossible.
Example: You need to travel 5 feet forward, but 10 minutes backwards in time to save your brother from tripping.
S = D/T
S = 5 feet/-10 minutes = -.5 feet per minute (FPM)
S = -.5 FPM
Travel at a negative speed? How can that be possible?
In conclusion, you'd need to travel at a negative speed to go backwards in time. Going faster would not allow you to move backwards in time because you would simply go further in time. However...
Making time a negative variable and Distance a negative variable as well, would keep speed at a positive variable.
e.g. You need to move backwards 5 from where you are and 10 minutes into the past to prevent your brother from falling.
S = -5/-10 = .5 FPM
S = .5 FPM
Very slow, but proves you can go backwards in time by traveling at a positive speed. Odd.
Here's another idea I had, but it's really really weird:
If you have the intent to move ahead 5 feet, but do not, then you are moving in negative speed. If you intend to move 5 feet in 10 minutes, at the 10 minute mark (if you have NOT moved) at that very instant, you'd be travelling at -5 FPM. This is ODD. Anyone wanna help shed some light on what I'm doing with my spare time here? Haha.
By the way, I now recall who said that you could travel at a speed to go back in time. That'd be Albert Einstein. This is gonna make me think up some stuff now...