To solve this problem, we will analyze each part of the question step by step. The key data provided is:

1. The magnitude of the electric field $E = 275 \, \text{N/C}$.
2. The charge of the electron $q_e = -1.6 \times 10^{-19} \, \text{C}$.
3. The mass of the electron $m_e = 9.11 \times 10^{-31} \, \text{kg}$.
4. The time for part (b) is $t = 1.25 \times 10^{-8} \, \text{s}$.

Part (a): Magnitude of the acceleration

Using the equation for the force on the electron in an electric field: $F = q_e \cdot E$

The acceleration $a$ can then be calculated using Newton's second law: $a = \frac{F}{m_e} = \frac{q_e \cdot E}{m_e}$

Substitute the given values: $a = \frac{(1.6 \times 10^{-19}) \cdot (275)}{9.11 \times 10^{-31}}$

Calculate: $a = \frac{4.4 \times 10^{-17}}{9.11 \times 10^{-31}}$ $a \approx 4.83 \times 10^{13} \, \text{m/s}^2$

Answer for (a): The magnitude of the acceleration is approximately $4.83 \times 10^{13} \, \text{m/s}^2$.

Part (b): Speed after $t = 1.25 \times 10^{-8} \, \text{s}$

The speed of the electron can be calculated using the formula for constant acceleration: $v = u + at$ where:

• $u = 0 \, \text{m/s}$ (electron starts at rest),
• $a = 4.83 \times 10^{13} \, \text{m/s}^2$,
• $t = 1.25 \times 10^{-8} \, \text{s}$.

Substitute values: $v = 0 + (4.83 \times 10^{13}) \cdot (1.25 \times 10^{-8})$ $v = 6.04 \times 10^{5} \, \text{m/s}$

Answer for (b): The speed of the electron after $1.25 \times 10^{-8} \, \text{s}$ is approximately $6.04 \times 10^{5} \, \text{m/s}$.

Let me know if you'd like more details on the calculations!

5 Follow-up Questions:

1. What is the physical meaning of the electric field in this problem?
2. How would the acceleration change if the electric field strength doubled?
3. How does the mass of the electron affect its acceleration?
4. How would this problem differ if the particle was a proton instead of an electron?
5. What would be the speed of the electron after $2.5 \times 10^{-8} \, \text{s}$?

Tip:

Always check the units when substituting values into equations, especially when