Final answer:
The particle undergoes an acceleration due to the electric force, which causes a change in its velocity. After calculating the forces and acceleration, the final speed of the particle at t = 2.0 s is found to be 20 m/s. option b is correct
Step-by-step explanation:
option b is correct The question concerns a particle with a mass of 4.0 g and a charge of 80 mC moving in a uniform electric field. The electric field has a strength of -2.5 N/C along the x-axis, and the particle has an initial velocity of 80 m/s along the same axis. To find the speed of the particle at t = 2.0 s, we need to calculate the acceleration caused by the electric force and then determine the final velocity.
First, we calculate the electric force (F) on the particle using F = qE, where q is the charge and E is the electric field strength:
F = (80 x 10^-3 C)(-2.5 N/C) = -0.2 N
The negative sign indicates that the force is in the direction opposite to the electric field. Next, we find the acceleration (a) using Newton's second law, F = ma:
a = F/m = (-0.2 N) / (4.0 x 10^-3 kg) = -50 m/s^2
The acceleration is in the opposite direction to the particle's initial velocity. Now, we can find the final velocity (vf) at t = 2.0 s using the equation vf = vi + at:
vf = 80 m/s + (-50 m/s^2)(2.0 s) = 80 m/s - 100 m/s = -20 m/s
The negative sign indicates that the particle has reversed direction. However, when we are asked for speed, we are looking for the magnitude of the velocity, which is 20 m/s. Therefore, the correct answer is (b) 20 m/s.