To solve for the acceleration of the electron, we can use the following kinematic equation, which relates acceleration, initial velocity, final velocity, and distance traveled:

$v_f^2 = v_i^2 + 2a d$

Where:

• $v_f$ = final velocity = $2.0 \times 10^7 \, \text{m/s}$
• $v_i$ = initial velocity = 0 (since the electron started from rest)
• $a$ = acceleration (what we need to find)
• $d$ = distance traveled = 0.10 m

Rearranging the equation to solve for acceleration $a$:

$a = \frac{v_f^2 - v_i^2}{2d}$

Substituting the known values:

$a = \frac{(2.0 \times 10^7)^2 - 0^2}{2 \times 0.10}$

$a = \frac{(4.0 \times 10^{14})}{0.20}$

$a = 2.0 \times 10^{15} \, \text{m/s}^2$

Therefore, the acceleration of the electron is:

$a = 2.0 \times 10^{15} \, \text{m/s}^2$

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the significance of constant acceleration in this context?
2. How does this compare to typical accelerations experienced in daily life?
3. How would you calculate the time it took for the electron to reach this speed?
4. How does relativistic motion affect high-speed electrons?
5. Can the same kinematic equations be used in non-uniform acceleration?

Tip: Always ensure units are consistent when solving kinematic problems.