AP Physics C 2017

Three! We can solve the problem.

Step 3 : Solve.
The rest of this problem is just algebra. Yes, you have to do it right, but setting up the problem correctly
and coming up with an answer that’s reasonable is more important than getting the exact right answer.
Really! If this part of an AP free-response problem is worth 5 points, you might earn 4 of those points just
for setting up the equation and plugging in values correctly, even if your final answer is wrong.

But which   equation    do  you use?    We  have    enough  information to  use **  (x −    x   0    =  v   0    t +    ^1  / 2  at     2   )   to

solve for t . Note that using ** means that we’ll have to solve a quadratic equation; you can do this with

the help of the quadratic formula.^4 Or, if you have a graphing calculator, you can use it to solve. But
almost always there’s a way to avoid the quadratic.

Algebra hint: You   can avoid   quadratics  in  all constant    acceleration    kinematics  problems    by  solving in

a   roundabout  way.    Try solving for the velocity    when    the watermelon  hits    the ground  using   *** 

then plug into * (v (^) f = v 0 + at ). This gives you the same answer.

What If Acceleration Isn’t Constant?

A typical Physics C kinematics question asks you to use calculus to find position, velocity, or acceleration
functions. Then you can solve a motion problem even if acceleration is not constant. The way to
remember what to do is, first and foremost, to understand graphical kinematics as discussed in the section
below. Then, we know that the slope of a graph is related to the derivative of a function; the area under a
graph is related to the integral of a function. Therefore:

• To find velocity from a position function, take the derivative with respect to time:

• To find acceleration from a velocity function, also take the time derivative:

• To find position from a velocity function, take the integral with respect to time:

• To find velocity from an acceleration function, take the time integral:

Most of the time, even on the Physics C exam, you’ll be able just to use the star equations to solve a
kinematics problem. Reserve your use of calculus for those problems that explicitly include an unusual
function for position, velocity, or acceleration.