# Phys 313 Quiz 6

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.
```