The concept of force as the rate of change of momentum is also vital in understanding wave phenomena, particularly in the context of sound waves. When a sound wave travels through a medium, it exerts a force on the particles of the medium, causing them to oscillate. The momentum of these particles changes as they move back and forth, and this change in momentum over time (caused by the force exerted by the sound wave) is what propagates the wave through the medium. In acoustics, this principle helps in understanding how sound waves can transfer energy over distances without the physical movement of the entire medium. For instance, in designing acoustic systems or studying sound insulation, this concept is used to calculate how sound waves exert forces on different materials, leading to energy transfer and sound propagation.

In sports, understanding and utilising the concept of force as a change in momentum is crucial for enhancing performance. For instance, in games like golf or tennis, players aim to maximise the change in momentum of the ball. By applying a force over a longer contact time with the ball (a longer swing), they increase the impulse, which consequently increases the ball's momentum and thus its speed and distance travelled. Similarly, in athletics, sprinters use forceful, quick strides to rapidly change their momentum and increase speed. In all these cases, the key is efficiently transferring the athlete's energy (force over time) to the object (ball, self) to maximise the change in momentum, thereby optimising performance.

A photonic rocket operates on the principle of force as a change in momentum, but instead of expelling conventional mass, it utilises photons (light particles). According to physics, photons have momentum despite having no rest mass. When a photonic rocket emits photons, it exerts a force due to the change in momentum associated with the emitted light. The photons moving in one direction impart a small but measurable momentum change in the opposite direction to the spacecraft. This concept is particularly attractive for space exploration as it provides a means of propulsion without the need for carrying conventional fuel. However, the force generated is extremely small because the momentum carried by photons is minuscule. Consequently, while the theory is sound, the practical application of photonic rockets in producing significant acceleration or in manned space travel is still a topic of research and development.

The design of safer cars heavily utilises the concept of force as the rate of change of momentum, particularly in features like crumple zones and airbags. In a collision, a car's momentum changes rapidly. Crumple zones are designed to deform in a controlled manner, increasing the time over which the momentum change occurs, thereby reducing the force experienced by the occupants. Similarly, airbags inflate quickly during a crash to increase the time taken for the occupant's momentum to reach zero. This longer duration reduces the force exerted on the occupants, minimising injuries. Engineers study collision dynamics to optimise these safety features, ensuring that they absorb and redistribute the forces of impact effectively, thereby protecting passengers by limiting the rate of momentum change.

The application of force as a change in momentum is fundamental in rocket and spacecraft technology. When a rocket burns fuel, it expels exhaust gases at high speeds in the opposite direction of its desired travel, creating a force on the rocket. According to Newton's third law, every action has an equal and opposite reaction. The momentum of the expelled gases (product of their mass and velocity) generates an equal and opposite change in momentum for the rocket, propelling it forward. This change in momentum over the time during which the force is applied (burn time of fuel) is essential in calculating the rocket's velocity and trajectory. It's not just the amount of fuel, but how quickly it is expelled that determines the rocket's speed and direction. In space, where there is little to no external resistance, even small forces can lead to significant changes in momentum, making precise calculations vital for manoeuvres and maintaining orbits.