Princeton Review 16th Edition PT1 Q18

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18) The question asks for the relationship between acceleration and distance when a charged particle is released from rest. Since we are dealing with charges and acceleration, we can try looking at the electric force of the system.

where k is Coulomb's constant, Q is the charge on one object, q is the charge on the second object, and r is the distance between the two objects

Now, let's use Newton's 2nd Law to solve for acceleration.

where m is the mass of the acceleration object

This may seem very complicated to try to graph, but there are only two variables that change, while the other variables are constants. Since they are constants, they will have no affect on the general shape of the graph. We can rewrite the equation as a proportion between acceleration and distance.

Our acceleration is inversely related to the square of the distance between the two charged particles. Graph A is the only graph that displays this relationship, so it must be our answer.

Answer: A