The most important formula from Newton's laws comes from the second, F=ma, or force equals mass times acceleration. There are variations of this, such as a=F/m or m=F/a but in effect they are the same equation, just solving for different variables. Force is measured in Newtons, mass in Kilograms, and acceleration in meters per second squared. Here are some practice problems.
1.) Find the force of a 3,650 kilogram train going 50 meters per second
First, you want to plug in the values you have, mass and acceleration: F=(3650)*(50)
Then, you simply multiply the values and add newtons to the end for force. F= 182,500 newtons
Now try to manipulate the equation for different values.
2.) Try to find the acceleration of a 1250 kilogram car with a force of 6000 newtons
Plug in your values 6000=1250a
Now get your variable on its own, and divide, and simplify 6000/1250=1250a/1250 4.8=a
So our acceleration is approximately 4.8 m/sec.
Further help for F=ma: https://www.youtube.com/watch?v=hO3UY9lrLkg And more example problems: https://www.youtube.com/watch?v=8Ghg1wOaPdY
Free Body Diagrams
Newton's laws also encompass the subject of free body diagrams.
For example, take this free body diagram to the left. This is could perhaps be a car, the applied force pushing the car forward and friction equally drawing it backward. The same is true of normal force and gravity, equally pulling at each other. Therefore, this object is moving at a constant velocity to the right. Here are some examples, try to describe a scenario in which each free body diagram could apply.
Net Force: Rightward Acceleration Ex: Car accelerating on a way to work at perhaps 10m/s2
Net force: Constant downward speed
Ex: A car falling out of a plane and tumbling down with no acceleration, perhaps at its terminal velocity
*Pictures from PhysicsClassroom.com*
Free Body Diagrams Video Tutorial: https://www.youtube.com/watch?v=25tJTmgYinM