Question

Given \( E(t) = 108t - 22 \), how is velocity derived from the electric field?

Hint:

To find the velocity from the electric field, integrate the electric field with respect to time, considering the charge and mass of the particle.

Answer 1

Step 1: The force on the charge is \( F = qE(t) \), giving acceleration \( a(t) = \dfrac{q}{m}(108t - 22) \).
Step 2: Velocity is the integral of acceleration over time: \[ v(t) = \int a(t)\,dt = \frac{q}{m}\int (108t - 22)\,dt \]
Step 3: Carrying out the integration term by term, \[ \boxed{v(t) = \frac{q}{m}\left(54t^2 - 22t\right) + C} \]