Let's imagine a skydiver jumping off of a plane. You can predict that the velocity of the skydiver will increase as he falls down, but will his speed increase infinitely if he does not open a parachute?
The answer is NO. After some time of falling, the skydiver will start to fall at a constant speed.
Let's take a closer look at the stages of falling to understand why the skydiver will eventually reach a constant speed.
Step I. All objects near the surface of the Earth experience a gravitational acceleration of 9.8m/s2. The skydiver is not an exception, and the skydiver accelerates due to the effect of gravitational acceleration.
Step II. As the speed of the skydiver increases, the drag force such as air friction increases. The skydiver is still accelerating, but the acceleration is decreasing due to air friction.
Step III. When the air resistance force equals the weight of the skydiver, the acceleration becomes zero. The skydiver reaches terminal velocity and falls at a constant speed. At this stage, the shape of the speed vs. time graph is a horizontal line, and the slope/gradient is zero.
Step IV. When the parachute is opened, the skydiver decelerates due to increased air resistance.
Step V. The skydiver slows down until the air resistance force and weight becomes equal again, and the skydiver reaches a new terminal velocity.
We can also draw a free-body diagram to illustrate this event.
Step I. When the object is just released from rest, the only force acting on the object is the gravitational force of the weight.
Step II. Air friction acts on the object as well, but the gravitational force is still bigger than the drag force, so there is acceleration.
Step III. When the air friction force equals the gravitational force from the weight, the net force acting on the object becomes zero. From Newton's second law (F=ma), the acceleration becomes zero since the net force is zero. Since there is no acceleration, the object is now falling down at a constant speed at the terminal velocity.