# Newton's 2nd Law: Why is Resistance Considered a Positive Force?

• Fakhro
In summary, the authors of this physics book say that the resistive force is opposite to the motion, and that the net force is equal to mass times acceleration, not just the resistive force.f

#### Fakhro

Homework Statement
An airboat with mass 3.50 3 102 kg, including the passenger,
has an engine that produces a net horizontal force of 7.70 3 102 N,
after accounting for forces of resistance (see Fig. 4.7). (a) Find the acceleration
of the airboat. (b) Starting from rest, how long does it take the
airboat to reach a speed of 12.0 m/s? (c) After reaching that speed, the
pilot turns off the engine and drifts to a stop over a distance of 50.0 m.
Find the resistance force, assuming it’s constant.
Relevant Equations
Newton's 2nd law of motion
regarding the last question.

I know that resistance is a negative force because it goes in the opposite direction to the movement of the boat. So whenever, I want to apply Newton's 2nd law of motion: the sum of forces = m a
I should write - F resit = m.a.
However, they have considered the resistance a positive force in this exercise. Why?

I should write - F resit = m.a
Are you talking about part (a) or part (c)? If it's part (a), Newton's second law says that the net force is equal to mass times acceleration, not just the resistive force. What is the net force in part (a)?
However, they have considered the resistance a positive force in this exercise. Why?
Please tell us who "they" are and exactly what "they" said. I agree that the resistive force is opposite to the motion.

• topsquark
Are you talking about part (a) or part (c)? If it's part (a), Newton's second law says that the net force is equal to mass times acceleration, not just the resistive force. What is the net force in part (a)?

Please tell us who "they" are and exactly what "they" said. I agree that the resistive force is opposite to the motion.
Sir, when I say the last question I mean C.
the problem is not of who are. "they".
the problem lies in the exercise. In the end, the resistance force was listed as a positive force when Newton's second law was applied. the sum of forces = m a / F resit = m.a.
whereas it should be written as - F resit = m.a.

This exercise is from a physics book. They mean the authors.

As I already said, you are right in saying that the resistive is opposite to the motion. If you have a number for the resistive force, say 50 N, then a correctly phrased answer would be "the resistive force is 50 N in a direction opposite to the velocity." That says it all. If the textbook gives you just a positive number as the answer, then it is incorrect because force is a vector that has magntude and direction.

For future reference, please post numbers, especially powers of 10, sing LaTeX. If you have not used LaTeX before, click in the link "LaTeX Guide", lower left. Numbers such as 3.50 3 102 kg are hard to interpret. Thank you.

• topsquark