AP Physics C 2017

the question:
“At first the ball is moving upward pretty fast, but the ball is slowing down while going upward.
(I know this because the speed is getting closer to zero in the first part of the graph.) The ball
stops for an instant (because the v–t graph crosses the horizontal axis); then the ball begins to
speed up again, but this time moving downward.”
Now, no numerical values were given in the graph. But would you care to hazard a guess as to the

likely slope of the graph’s line if values were given?^6

Figure 11.1 Graphs

The position–time graph has a changing slope, so the speed of the object is changing. The object starts
moving one way, then stops briefly (where the graph reaches its minimum, the slope, and thus the speed is
zero). The object then speeds up in the other direction. How did I know the object’s velocity changed
direction? The position was at first approaching the origin, but then was getting farther away from the
origin.
The second graph is a velocity–time graph, and it must be analyzed differently. The object starts from
rest, but speeds up; the second part of the motion is just like the example shown before, in which the
object slows to a brief stop, turns around, and speeds up.

Air Resistance and the First-Order Differential Equation

The force of air resistance is usually negligible in kinematics problems. You probably don’t believe me,
though. After all, unless you’re on the moon, or unless your teacher is using a vacuum chamber for
demonstrations, air is all around us. And if I dropped a piece of paper simultaneously and from the same
height as a lead weight, the weight would hit the ground first—and by a huge margin. Certainly.
Obviously.
Why don’t you try it? But be sure you crinkle up the paper first and drop it from about waist height.
Notice how the lead weight hits the ground WAY before ...
Oops.
The weight and the paper hit the ground essentially at the same time. If the weight did hit first, the
difference wasn’t anything you could reliably time or even be sure enough to gamble on.
Conclusion: As long as we’re not throwing objects out of our car on the freeway, air resistance is not
important in kinematics.

The most    common  questions   asked:

When    is air  resistance  important?  And how should  it  be  dealt   with?

Air resistance  should  only    be  considered  when    the problem explicitly  says    so. Usually,    a   problem will

suggest that    the force   of  air acts    opposite    to  an  object’s    velocity,   and is  equal   to  a   constant    times   the

velocity: F (^) air = bv .^7