First off, thank you for even trying.... For some reason, I can't let question go. I usually can figure it out, but whatever.
Q) according to aristotle, objects @ rest tend to remain @ rest. It follows that if an object is released from rest and falls vertically, it shouldn't fall, since it's natural tendency to stay @ rest. This statement is:
A)true; obj released and allowed to fall doesn't really start from rest, it's an approximation we make.
B) true, if we lived in a vacuum.
C) false, galileo demonstrated that an obj's natural tendency is to remain in motion
(*seemed right @ the time)
D) false, it's possible for the velocity of an obj to be zero while the rate of chage of velecity is not zero. (Wtf...)
I put C, correct is D.
Ok, so for this question, I would firstly eliminate A and B, because you know that Aristotle is wrong, so it has to be false.
Then for C, Newton's first law states that objects in motion tend to remain in motion AND objects at rest tend to remain at rest. So, question C is a half-truth. It doesn't account for objects at rest staying at rest. It is making the assumption that objects are always in motion.
With this in mind you should eliminate choice C as an answer choice, then it really doesn't matter what D is, because you know it's not A, B, or C, so it has to be D.
But in looking at D. Think about Velocity. It is Displacement/time. NOT distance over time, this is because velocity is a vector quantity. It has to have both magnitude AND direction. So, for an object that starts out at point A, travels 100 miles south to point B, then 100 miles north back to point a in 100 seconds, would set up a formula like this:
Total displacement = 0, because you end up where you started. Total distance on the other hand is 200 miles, but velocity looks at displacement, not distance.
So, now you set your displacement over time:
0m/100s = 0 m/s So now your velocity is zero, but the rate of change in velocity is not, because had you taken your velocity equation from 40s when you were still heading south, there would be a net velocity.
It's weird to think about, but you just have to remember that velocity is a vector, so if you end where you start you have zero direction, thus you have zero displacement (because by the nature of displacement, you have to be "displaced" meaning moved to some other point).
This is why D makes sense, but remember, you didn't even need to know why D worked, just that the other three violated Newton's 1st law.
Hope that helps.
