CollegeBoard SAT Physics Study Guide PT1 Q45

CollegeBoard's Book

45) We need to find the relation between the two charged particles in the situation described in the problem. This question requires us to know Newton’s 2nd Law as well as the relation between an electric field and electric force.

Where F is force, m is mass, a is acceleration, q is charge, and E is electric field

Let’s start by relating the 2 above equations.

Where m is mass, a is acceleration, q is charge, and E is electric field

If we divide both sides by mass(m) and electric field(E) we will get this equation.

Where m is mass, a is acceleration, q is charge, and E is electric field

Since the two objects travel the same distance in the same amount of time, and since they both start from rest and travel with a constant acceleration, we can deduce that they must also travel with the same magnitude of acceleration. The problem also states that they move in a uniform electric field.

Now that we have shown that the acceleration and electric field are the same for both particles, we know that the value of q/m will also be the same for both particles. q/m is the ratio of the charge to the mass, so our answer is E.

Answer: E