An example of Newton's second law of motion would be if someone's car ran out of gas and they tried to push it and, because the car is much heavier, it would require more force to push than if it was a lighter object, like a bicycle. This example relates to Newton's second law of motion because this law stipulates that the heavier an object is, the more force will be required to move the object and give it acceleration.
This is a simple concept to understand because people have experienced trying to move objects that are heavier than others. Heavier objects simply require more force to move.
What some people don't know, however, is that Newton's second law of motion is actually written out in a very simple equation that allows scientists to calculate the amount of force needed to move an object of a certain weight at a certain rate of acceleration. The formula is written out as force being equal to the mass times the acceleration. So, if the mass and the rate of acceleration is known, the force can be calculated. The force is written in newtons.
An example of this formula being put to work could use the simple example of someone trying to move a car. If the car weighs 1,000 kilograms and the person is trying to accelerate it to a rate of .05 of a meter per second, then .05 multiplied by 1,000, or the acceleration times the mass, would equal 50 newtons, which is the amount of force that would be required.