Definition of Impulse: Impulse is defined as the product of the force applied and the time interval over which the force acts. Mathematically, this is expressed as Impulse = F Δt.

Relationship between Impulse, Force, and Time: Impulse is equal to the change in momentum of an object. Therefore, impulse is directly proportional to the force applied and the time over which the force acts. This means that:

• If the force is greater, the impulse will be greater.
• If the time over which the force acts is longer, the impulse will be greater.
• The impulse is the same regardless of the force applied, as long as the time of impact is the same. This is why using a larger racket (increasing the time of impact) reduces the force felt by the ball.

Concept: Resultant force is defined as the change in momentum of an object per unit time. Momentum (p) is given by the product of mass (m) and velocity (v): p = mv. Therefore, a change in momentum (Δp) is a change in mass * velocity. The change in momentum occurs over a period of time (Δt).

Equation: The equation relating resultant force (F), change in momentum (Δp), and change in time (Δt) is: F = Δp / Δt

Answer: Resultant force is the change in momentum of an object per unit time. It is defined as F = Δp / Δt, where Δp is the change in momentum and Δt is the time interval over which the change occurs.

Solution:

We can use the principle of conservation of momentum. The initial momentum of the system is due to the moving block only. The final momentum is due to the combined mass moving at a final velocity.

Initial momentum (p_i) = m₁ * v₁ = 2.0 kg * 3.0 m/s = 6.0 kg m/s (to the right)

Final momentum (p_f) = (m₁ + m₂) * v_f = (2.0 kg + 3.0 kg) * v_f = 5.0 kg * v_f

Since momentum is conserved, p_i = p_f. Therefore:

6.0 kg m/s = 5.0 kg * v_f

v_f = 6.0 kg m/s / 5.0 kg = 1.2 m/s (to the right)

Therefore, the velocity of the combined blocks immediately after the collision is 1.2 m/s to the right.