A good example that illustrates the law of acceleration is a car's increasing velocity. When a person pushes down the gas pedal, the car has positive acceleration. When the brakes are applied over a period of time, the vehicle accelerates in the negative direction. Another example is throwing a football. It travels in the direction of the line of action of a throw’s force at a speed that’s inversely proportional to the football’s mass and directly proportional to the force.
Additionally, when a person steps on a weighing scale, the number that appears on the scale is not exactly the person’s mass, which remains constant. It is his weight, and this changes under different accelerations. This is the reason why astronauts on the moon weigh differently than on earth.
When a person pulls a wagon containing a lesser weight than himself, the wagon's velocity changes, producing a positive acceleration. This acceleration is limited by the strength of the external force on the system.
An example of generating an external force to accelerate is the use of roller skates. It’s hard to get going when a person keeps the skates pointing forward with only the wheels in contact with the ground. To start moving, a sideways push on the wheels is necessary. However, wheels can’t turn sideways, so the person should push against the ground. This way, he will start to accelerate.