Final answer:
To determine the acceleration of the proton, we can use Newton's second law, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. The electric force can be calculated using the formula F = qE, and the acceleration can then be found using the formula a = F/m. The initial speed of the proton can be calculated using the equation of motion v^2 = u^2 + 2as, and the time interval over which the proton comes to rest can be found using the formula t = v/a.
Step-by-step explanation:
To determine the acceleration of the proton, we can use Newton's second law, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the force is the electric force exerted on the proton by the electric field. The electric force can be calculated using the formula:
F = qE
Where F is the force, q is the charge of the proton, and E is the electric field.
The acceleration can then be found using the formula:
a = F/m
Where a is the acceleration, F is the force, and m is the mass of the proton.
Since the protons mass is approximately 1.67 × 10^(-27) kg, the acceleration of the proton in this case would be -3.31 x 10^17 m/s^2 in the negative x-direction.
To calculate the initial speed of the proton, we can use the equation of motion:
v^2 = u^2 + 2as
Where v is the final velocity, u is the initial velocity (which is 0 in this case since the proton starts from rest), a is the acceleration, and s is the distance traveled by the proton before it comes to rest. Solving for v:
v = sqrt(2as)
Substituting the known values, we find that the initial speed of the proton is approximately 8.15 x 10^5 m/s in the positive x-direction.
The time interval over which the proton comes to rest can be found using the formula:
t = v/a
Where t is the time interval, v is the initial velocity, and a is the acceleration. Substituting the known values, we find that the time interval is approximately 4.92 x 10^(-23) s.