Final answer:
The equation connecting change in momentum, force, and time is F Δt = Δp, derived from Newton's Second Law of Motion in terms of momentum. To find the change in momentum (Δp), substitute mass and velocity changes into the formula Δp = m(v_final - v_initial). The force can be calculated with F = Δp/Δt if the time interval is known.
Step-by-step explanation:
The equation that connects change in momentum, force, and time is rooted in Newton's Second Law of Motion when expressed in terms of momentum. This relationship is encapsulated by the Impulse-Momentum Theorem, which states that the impulse (force times time) applied to an object is equal to the change in momentum of that object. The fundamental formula is F Δt = Δp, where F is the force applied, Δt is the time interval over which the force is applied, and Δp is the change in momentum (m Δv, mass times the change in velocity).
To calculate the change in momentum, we substitute the values for the object's mass and its initial and final velocities into the equation Δp = m(v_final - v_initial). Once we have the change in momentum, we can use it to find the average force exerted during the time interval with the formula F = Δp/Δt, assuming we know the duration of time over which the force was applied.