AP Physics C: E&M
9.3 Conservation of Electric Energy
Ion 1 with charge \(+q\) and Ion 2 with charge \(+2q\) each have mass \(m\) and enter a region of uniform electric field with identical initial kinetic energy \(K_0\). The electric field is directed opposite to the initial velocity of each ion, exerting an electrostatic force that brings them momentarily to rest. Ion 1 comes to rest after traveling a stopping distance \(d_1\) with an acceleration of magnitude \(a_1\). Which row in the table correctly relates the stopping distance \(d_2\) and the magnitude of the acceleration \(a_2\) of Ion 2 to those of Ion 1?
| Row | Stopping Distance \(d_2\) | Acceleration Magnitude \(a_2\) |
|---|---|---|
| A | \(\dfrac{1}{2} d_1\) | \(2 a_1\) |
| B | \(\dfrac{1}{2} d_1\) | \(\dfrac{1}{2} a_1\) |
| C | \(d_1\) | \(2 a_1\) |
| D | \(2 d_1\) | \(2 a_1\) |
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