A particle (mass = 4.0 g, charge = 80 mC) moves in a region of space where the electric field is uniform and is given by Ex = -2.5 N/C, Ey = Ez = 0.If the velocity of the particle at t = 0 is given by vx = 80 m/s, vy = vz = 0, what is the speed of the particle at t = 2.0 s?
A)40 m/s
B)20 m/s
C)60 m/s
D)80 m/s
E)180 m/s

Question

Quizplus · Accepted Answer

First, we can calculate the acceleration of the particle using the electric field:
a = qE/m = (0.080 C)(2.5 N/C)/(0.0040 kg) = 50 m/s^2
Then, we can use the kinematic equation:
v = v0 + at
where v0 is the initial velocity (in the x-direction). Substituting the given values, we get:
vx = v0x + axt
80 m/s = v0x + (50 m/s^2)(2.0 s)
Solving for v0x, we get:
v0x = 80 m/s - (50 m/s^2)(2.0 s) = -20 m/s
Note that the negative sign indicates that the particle is slowing down in the x-direction.
Next, we can use the conservation of energy to find the final speed of the particle. Since there is no potential energy in the electric field, the initial kinetic energy (K1) is equal to the final kinetic energy (K2):
K1 = K2
(1/2)mv0x^2 = (1/2)mv^2
Solving for v, we get:
v = v0x/sqrt(2) = (-20 m/s)/sqrt(2) = -14 m/s
Note that the negative sign indicates that the particle is moving in the opposite direction to its initial velocity. However, the question asks for the speed (magnitude of velocity), so we take the absolute value:
|v| = 14 m/s
Therefore, the speed of the particle at t = 2.0 s is approximately 14 m/s, which is closest to choice B (20 m/s).

A Particle (Mass = 4