A rapid change in speed (that is, a large acceleration) requires a large force, especially if the thing that is changing its speed is massive. We use this idea to push a nail into a piece of wood. The force required is inconveniently large: you can't do it with your fingers. But it's easy when you use a hammer. Assume the nail does not move. The moving hammer will have to abruptly stop, in a few thousands of a second. It has mass and it has speed: therefore the force that the nail must exert on the hammer is huge. The Law of Interaction tells us that the hammer will also exert a huge force on the nail.

Consider the statement, "It's hard to stop a speeding locomotive." This is a reference to the Law of Motion: the locomotive is massive and it is speeding, but we wish to stop it. To do this at all quickly will require a very large force: it's hard.

On a curvy mountain road, the state traffic engineers place signs recommending lower speeds at the sharper curves. It is their hope that you will not obey the Law of Inertia, continuing in a straight line, but instead change direction as you go around the curve. But then, according to the Law of Force and Acceleration, the car wheels will have to exert a force in the direction of the acceleration (towards the inside of the curve). The acceleration will be larger when the velocity is larger, both because there is more velocity to change, and because a faster car goes through the curve in less time.

You will find that you can't drive very fast on a bumpy road -- it doesn't seem safe, and it certainly is uncomfortable. The Law of Force and Acceleration can explain this:
Assume we have little bumps 1 cm high, that are 1 m apart, and that the car is travelling at 10 m/sec. Then it only takes 1/10 second to get from one bump to another; the car will go bumpbumpbumpbumpbump faster than you can say it. In each 1/10 second the wheels move up and down 1 cm (and we would, too, if we didn't have springs and shock absorbers). So the wheels are down, and then 1/20 second later they are 1 cm higher, and then 1/20 second later again they are low again. The wheels move up 1 cm in 1/20 second and then down in 1/20 second. The up-and-down speed is (about) 20 cm/second. The speed also is changing, from up to down in 1/20 of a second; the change is velocity is 40 cm/sec and the acceleration is 8 m/sec^2. This is a rather large acceleration -- it is almost the acceleration of a freely falling object, and you will indeed feel that you are leaving your tummy behind. In reality, the springs and shock absorbers get rid of most of this, but you will not be able to go faster, because this decreases the time interval and makes the vertical speed and acceleration larger.

The unit on the Law of Force and Acceleration