How Force and Mass Change Acceleration

By the end of this lesson, you will be able to use Newton's Second Law of Motion to calculate how much an object speeds up when you know the push on it and how much matter it contains.

Picture yourself at the grocery store pushing an empty cart down the aisle. One easy push and the cart takes off quickly. Now imagine that same cart loaded with twenty bags of groceries. You push just as hard, but the cart barely gets going. That everyday difference is exactly what Newton's Second Law describes.

Newton's Second Law says that acceleration, which is how quickly an object's speed or direction changes, depends on two things: the net force acting on the object and the object's mass. Net force is the total of all forces pushing and pulling on an object after opposite forces cancel each other out. Mass is the amount of matter in an object, measured in kilograms. The law is written as force equals mass times acceleration, or F equals m times a.

To find acceleration, you rearrange the equation: acceleration equals net force divided by mass. Force is measured in newtons, and acceleration comes out in meters per second squared. So if you push an empty 10 kilogram cart with a net force of 30 newtons, the acceleration is 30 divided by 10, which equals 3 meters per second squared.

Now load that cart until its mass is 30 kilograms and push with the same 30 newtons. The acceleration becomes 30 divided by 30, which is only 1 meter per second squared. Notice the pattern: when net force goes up and mass stays the same, acceleration goes up. When mass goes up and force stays the same, acceleration goes down.

Try it: If a net force of 12 newtons acts on a 4 kilogram box, what is the box's acceleration?