According to the impulse-momentum theorem, the impulse applied to an object is equal to the change in its momentum. Impulse is defined as the product of force and time (F × Δt). Since both the force and the time interval are identical for both objects, the impulse delivered to each object is the same, resulting in an identical change in momentum for both.

Momentum (p) is defined as the product of mass (m) and velocity (v), expressed as p = mv. Since both objects have the same velocity, the momentum is directly proportional to the mass. Given that the mass of B is twice the mass of A (mB = 2mA), it follows that the momentum of B must be twice the momentum of A (pB = 2pA).

A rocket operates based on the principle of conservation of linear momentum. As the rocket expels exhaust gases at high velocity in one direction, it experiences an equal and opposite reaction force, known as thrust, which propels the rocket forward. Since the total momentum of the system (rocket plus fuel) remains constant in the absence of external forces, the rocket gains forward momentum.

In classical mechanics, linear momentum (p) is defined as the product of an object's mass (m) and its velocity (v), expressed by the formula p = mv. Since momentum is a vector quantity, it depends directly on both the scalar property of mass, which represents the object's inertia, and the vector property of velocity, which describes the object's speed and direction of motion.

Momentum is a vector quantity defined as the product of an object's mass and its velocity. It represents the quantity of motion an object possesses. Mathematically, it is expressed as p = mv, where m is mass and v is velocity.

According to Newton's Second Law of Motion, the net force acting on an object is equal to the rate of change of its momentum with respect to time. Mathematically, this is expressed as F = dp/dt. This relationship provides a more generalized definition of force that applies even when mass is changing, such as in rocket propulsion.

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Momentum is defined as the product of mass and velocity (p = mv). If the mass remains constant and the velocity is doubled, the new momentum becomes p' = m(2v) = 2mv, which is exactly twice the original momentum. While kinetic energy (K.E = 1/2mv^2) would quadruple, the momentum increases linearly with velocity.

The relationship between kinetic energy (K) and momentum (p) is given by p = sqrt(2mK). For a constant kinetic energy, momentum is directly proportional to the square root of the mass (p ∝ sqrt(m)). Since the α-particle has the largest mass among the listed particles (electron, proton, deuteron, and α-particle), it will have the highest momentum for a given kinetic energy.

Newton's Second Law states that the net force applied to an object is equal to the time rate of change of its linear momentum. Mathematically, F = dp/dt. Since momentum is mass times velocity, this change in momentum results in acceleration for constant mass.