Kate's inertial mass exerted a force on the safety belt, causing the safety belt to exert an equal and opposite force on Kate. It makes more sense vice versa, though. Kate's inertia caused her to continue to move forward even though the car was slowing down. The safety belt exerted a force back onto her to overcome this inertial force being applied on it by Kate.
Inertia
'The car's inertia carried it forward several feet after the driver pushed the brakes.
'The car's inertia carried it forward several feet after the driver pushed the brakes.' 'His inertia launched him forward after reaching the base of the hill.'
law of inertia
When the bus driver applies brakes suddenly, the passengers move forward on account of inertia.
The answer, in short, is INERTIA. Inertia is resistance to changes in motion, and is proportional to mass. Newton's 1st Law of Motion tells us that objects in motion will remain in motion (in a straight line) unless acted upon by an external force. In the example given, the passengers (objects) pitch forward when the driver hits the brakes in a forward-moving car (providing the external force) because their bodies possess inertia separate from the inertia of the moving car. The car slows down due to the braking, but the passengers' separate inertia(s) will cause them to keep moving forward until restrained by an outside force (seatbelt, dashboard, windshield, etc.) Larger, heavier passengers will pitch forward with more force (inertia is proportional to mass, remember?).
Inertia of Motion
To replace brakes effectively, you need to know what type of brakes you have. In general, you will need a jack, new brakes, a wrench and Allen wrenches.
Inertia. A body in motion will remain in motion unless acted upon by an outside force. The motion of the bus is stopped by the brakes. The person inside keeps moving as it is not being braked.
inertia
Inertia is the resistance to a change in motion. Most likely you've felt this in a car when it speeds up quickly and it feels like you're sinking into the seat back. Or, when the car brakes hard and your body moves forward. The relationship between inertia and mass is that the greater the mass, the greater the inertia.
There is no such thing as "force of inertia". The passengers are thrown forward, maintaining their initial motion. This is an application of Newton's First Law, which states that an object in motion stays in motion unless acted upon a force. The force of the car brake is acted upon the car and not on the passengers. This is why the passengers continue to move forward for a second when the car stops.