Why do cars running very fast in a curve road tend to move out of the road in a path tangential to the curve road?

Velocity is a vector, meaning that along with the measurement of speed in meters/second, it also needs a direction. If a car was driving North at 10ms-1 that would be its velocity at that point. The car then turns left so it's travelling west at 10ms-1. The car's velocity has changed, therefore there must have been some acceleration for the car's velocity to have changed. That acceleration is always towards the middle of the circle that it is turning