Conservation of Momentum Problem

[Avefan]

Homework Statement

The same horizontal force is applied separately to two objects initially at rest on a horizontal, frictionless surface. Object A has less mass than object B. In each case the force is applied for the same length of time. Which of the following statements is true after the push?

(a) Object A has greater momentum than object B.
(b) Object B has greater momentum than object A.
(c) Object A has the same momentum as object B.
(d) Object A has the same kinetic energy as object B.
(e) Both objects have no momentum.

Homework Equations

p = mv
delta_p = integral(F dt)

The Attempt at a Solution

The answer key solution to this problems is option c with the explanation that "since the both objects are given the same force over the same period of time, F = dp/dt , delta_p_a = delta_p_b."
However, why is delta_p(change in momentum) the same as momentum and why isn't option (b) a plausible answer?

 

[FactChecker]

Homework Statement

The same horizontal force is applied separately to two objects initially at rest on a horizontal, frictionless surface. Object A has less mass than object B. In each case the force is applied for the same length of time. Which of the following statements is true after the push?

(a) Object A has greater momentum than object B.
(b) Object B has greater momentum than object A.
(c) Object A has the same momentum as object B.
(d) Object A has the same kinetic energy as object B.
(e) Both objects have no momentum.

Homework Equations

p = mv
delta_p = integral(F dt)

The Attempt at a Solution

The answer key solution to this problems is option c with the explanation that "since the both objects are given the same force over the same period of time, F = dp/dt , delta_p_a = delta_p_b."
However, why is delta_p(change in momentum) the same as momentum and why isn't option (b) a plausible answer?

Both objects start at rest so the initial momentum of both is 0 (i.e. initial_p=0). So at any time, delta_p = current_p - initial_p = current_p - 0 = current_p
Of course, (c) contradicts (b), so (b) can not be true.