# Law of Force and Acceleration - Newton's Second Law of Motion

###### Explanation

According to **Newton s Second Law of Motion**, also known as the **Law of Force and Acceleration**, a force upon an object causes it to accelerate according to the formula *net force = mass x acceleration*. So the acceleration of the object is directly proportional to the force and inversely proportional to the mass.

###### Transcript

Law of force and acceleration this is also known as Newton's second law of motion. There's 3 components to Newton's second law. The first one is that a force on an object will cause that other to accelerate, the second is this acceleration is directly proportional to the force so the harder I push, the harder it accelerates okay. The third is this acceleration is inversely proportional to the mass of the object so if I'm pushing an empty shopping cart I'm going to be able to get it to go a lot faster than if I'm pushing a shopping cart that's full of groceries.

Okay, so it makes sense and we can show this relationship by Newton's formula over here, force equals mass times acceleration okay. So let's do a practice problem that you might see which is a good application of Newton's second law of motion okay. Let's say we have a rocket in space so there's no air resistance or anything, it's accelerating at 40 meters per second but while it's accelerating it's losing mass because it's burning fuel. The fuel is actually becoming a thrust that's causing it to accelerate so at point where it burns up half its mass due to fuel loss and the thrust is tripled what is the acceleration going to be at that point okay?

Well if we say that force is mass times acceleration and we say that the force the thrust is tripled during this time but the mass is decreased by one half then what happens to the acceleration okay, so we're going to say x is the change in acceleration okay. Well if I say this increase is by 3 and this decrease is by one half then our acceleration must increase by 6 times. So 6 times 40 meters per second is 240 meters per second squared which is the acceleration at that point and time. And that's one of the reasons rockets do accelerate in space because they're losing mass that loss of mass conversely increases their acceleration okay? So this is a good practice problem that kind of demonstrates Newton's second law of motion.