Understanding Air Resistance: Explaining the Math Behind Reduced Force

[brake4country]

Can someone please explain the math of this problem?

-If F is the force of air resistance on an object with mass m moving at a constant velocity, which of the following best describes the acceleration of the object when the force of air resistance is reduced by a factor of 4?
(a) F/m
(b) 1/2 F/m
(c) 1/4 F/m
(d) 3/4 F/m

The answer is d but I do not understand how to get it. Thanks in advance!

 

[Travis_King]

If it is moving at a constant velocity, what force is required in order to maintain that velocity in the initial case (with full air resistance)?

If the Air resistance is reduced by a factor of four, but the same force is assumed to be acting on the object, how does the object react?

 

[brake4country]

I am assuming that when velocity is constant, then the F(air) must cancel out the F of (mg). Therefore, when I drew this out on paper, I made the F(mg) component longer and the F(air) shorter since F(air) is reduced.

How do the fraction come into play? How is the answer 3/4 F/m? Thanks in advance

 

[jbriggs444]

I am assuming that when velocity is constant, then the F(air) must cancel out the F of (mg). Therefore, when I drew this out on paper, I made the F(mg) component longer and the F(air) shorter since F(air) is reduced.

How do the fraction come into play? How is the answer 3/4 F/m? Thanks in advance

What is the net force remaining when you reduce the air resistance by a factor of 4?

 

[brake4country]

I get it. Reducing by a factor of 4 requires one to think in terms of fractions (1/4). Therefore, the net F remaining is 3/4. Thanks again!