Explain why you are accelerating and yet going the same speed.
Acceleration occurs if there is a change in speed, or if there is a change in direction. While your car's speed doesn't change, its direction does. So it experiences an acceleration.
It all has to do with Newton's first law. The law basically says a body moving in a straight line at constant speed will continue to move in the same direction and at the same speed unless acted upon by an external force. This is due to the inertia of the body.
In order for your car to change direction it must be subjected to an external force. That force is the static friction force between your tires and the road, which is called the centripetal force, that allows you to change direction by continually pulling the car towards the center of the circular path of the car. The centripetal force opposes the centrifugal force (apparent force) that wants to keep the car moving in its original direction and speed, and that is really the inertia of the car. The centripetal force causes a centripetal acceleration towards the center the magnitude of which is
Where $v$, in your case, is 65 mph, and $r$ is the radius of the circular path, which depends on how sharp a turn the car makes. The sharper the turn the greater the centripetal force and centripetal acceleration.
Hope this helps.