What causes acceleration to increase?

Answer 1

I am assuming you actually did mean acceleration and not speed or velocity. Acceleration already implies a change in speed or velocity, either increasing or decreasing. For an object to change speed -- in other words, for an object to accelerate -- the sum of the forces acting upon it must be non-zero. But you asked about an increase in acceleration! That's a bit different. The change in acceleration is called jerk, which requires a bit of explanation. If you drop an object off a tall tower in a vacuum on Earth, that object will experience constant acceleration; that is, its speed will increase at a constant rate. At the end of its first second of freefall, it will achieve a speed of 32 feet per second; at the end of its second second of freefall, it will reach 64 feet per second; and at the end of its third second, it will be falling at 96 feet per second. You can see that the change in speed from one second to the next is always 32 feet per second, which implies a constant acceleration. Since the object is accelerating, we know that the sum of the forces acting upon the object is something other than zero. In fact, the force acting upon the falling object is its weight, and since there's nothing to counteract its weight, the object falls at constantly increasing speed. But what if the object reached 32 feet per second in the first second and 64 feet per second in the next and 128 feet per second in the next?! You can see that the difference in speed from one second to the next is not constant; it's increasing. That implies that the force acting on the object is not constant but is also increasing. That sort of thing happens in rocketry -- think of the space shuttle -- when the thrust forces created by the rocket motors increase greatly as they burn off fuel. A varying force will result in a varying acceleration, which is called jerk.