A proton is fixed at **x = 0**.
Another proton is held at **x = 1 m**,
and then released.

**
Question 1
**

Is the acceleration of the second proton constant as it moves
from **x = 1 m**
to **x = 2 m**?

Answer: no, the acceleration decreases

**
Question 2
**

Write an expression for the acceleration of the second proton
when it is at **x = x0**, some point between **x = 1 m**
and **x = 2 m**.

k * q1 * q2 k * e * e Answer: Force = ----------- = ---------- r^2 x0^2 F k * e^2 accel = --- = ----------- m x0^2 * m

**
Question 3
**

Which of these is closest to the time for the proton to reach **x = 2 m**?

A: 1 s B: 5 s C: 10 s D: 50 s

Answer: The maximum acceleration occurs when the proton is at x = 1 m, and has magnitude 0.14 m/s^2. If the proton accelerated at this (high) rate for the entire journey, it would take 2 * 1 m t = sqrt(-----------) = 3.8 sec 0.14 m/s^2 The minimum acceleration occurs when the proton is at x = 2 m, and has magnitude 0.034 m/s^2. If the proton accelerated at this (low) rate for the entire journey, it would take 2 * 1 m t = sqrt(-----------) = 7.6 sec 0.034 m/s^2 Since the actual acceleration varies between these two limits, the time it takes to make the journey must between the two limits. B = 5 seconds is closest.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.