Mail time: using a fourth kinematics equation on the AP exam?

More mail about motion:

I was wondering if I could ask you an AP exam question.  I see on your algebraic kinematics information to memorize that the 3 given equations are on the AP equation sheet.  The fourth equation that 'may occasionally be useful' is not on the equation sheet.*  If students were to need it for a question on the AP exam, would it be provided?  Or would they need to derive it from the other 3 given equations?

*This is the equation x =  t(vf+vo)/2 

Also, do you allow your students to use the AP table of equations on the daily quiz?  Or do you expect them to have those equations memorized? 

Students are not allowed to use the equation sheet on the quizzes (though I do let them use handwritten notes, so many write the equations out).  My students get the equations for tests.  They memorize these equations through use, generally, though I don't formally "require" them to be memorized.

As for that fourth equation, it's really using the definition of average velocity with constant acceleration.  The exam will not give this equation, but it can be used if students know it.  It *can* be used as a starting point for a derivation or a justification.

Mail time: airplane and car with the same acceleration, which moves faster?

A summer institute participant asks: 

I had a quick physics question from one of your daily quizzes: Which is moving faster, a car with an acceleration of 2 m/s/s, or an airplane with an acceleration of 2 m/s/s? My answer was airplane but my students are not happy with that answer. Is there any way you could explain it to me so I make sure I am telling them the correct answer?

Awesome, important question - this is a "holy grail" question for understanding motion.  

Acceleration tells the CHANGE in speed every second.  Both the car and the airplane gain 2 m/s of speed each second.  

But this doesn't say how fast either moves!  Sure, if the airplane is cruising and speeds up a bit, while the car is entering the freeway, the airplane moves faster.  But, say the airplane is starting from rest on the runway, and speeds up to 2 m/s after one second, 4 m/s after two seconds, etc.  Then say the car is on the freeway.  The car is initially moving 30 m/s, then 32 m/s, then 34 m/s, etc.  The car is moving faster - yet the objects have the same acceleration!

Hope this helps.  The answer is, WE DON'T KNOW.

GCJ

Don't make agreements you aren't willing to fulfill

In spring of 2021, a student asked me, "Hey, Mr. Jacobs, if we *all* pass the AP exam, can we cut your hair?"  I said, "sure."  The odds of every one of my 15-20 9th graders passing the AP Physics 1 exam were not great.  Not insurmountable, but unlikely.  And lo, that year most students did pass, but a couple did not.

I made the same deal with my class in 2022.  And again in 2023.  

But, whoops.  In early July I got the score report - all 17 students got 3s and above.  Gulp.  

A promise is a promise.  

It will grow out.  Eventually.  Congratulations to an awesome class.