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Braking acts to slow an object, so acceleration of the truck and the cartons is in the opposite direction as the velocity.
The braking force acts directly on the truck and is transmitted to the cartons through friction.
Do notice that there is a forward force on the lower carton in addition to the frictional force acting backwards on it, and so you do need to justify to yourself that it doesn’t affect that answer.
Regardless, this problem is provided as a sample because it illustrates how you would apply Newton’s 2nd and 3rd Law in a wide variety of problems that you might be asked to solve on your homework, and so it is worth looking at the mathematical analysis. At the start of the problem, the truck and both cartons are traveling forward.
You can use this tool as a coefficient of friction calculator, too.
Static friction acts when the object remains stationary. If we don't take friction into account, even the smallest force should cause some acceleration of the box according to Newton's second law.
It is based on a simple principle: the friction is proportional to the normal force acting between the object and the ground.
Learn how to apply the force of friction equation and what is the difference between static and kinetic friction.
In reality, you need to pull quite hard for the box to start moving because of the static friction force.
Kinetic friction acts on a moving object or, in other words, on an object with nonzero kinetic energy.