You need a lot more information than that. What design of robot? What sort of "servo motors"? How are you going to power the robot? How much time do you have? What experience of programming and building robots do you have? And most important - what are the rules of the two competitions?
Pure speed is very easy to program. Provide a lot of power and run the motors at full speed until you hit something or run out of power. But I bet there's more to it than that.
Steve