When an airplane during takeoff, the distance traveled is not proportional to time. This is because the airplane's acceleration varies during takeoff.
When a ball is tossed up in the air and falls back to the ground, the distance traveled is also not proportional to time. This is because the ball's acceleration is due to gravity, which is constant.
However, your speed while riding on a roller coaster is proportional to time. This is because the roller coaster's speed is constant throughout the ride.