Answer :
Final answer:
To stop a 920-kg car moving at 95.7 km/h within a distance of 126 m, a force of approximately 2572 N is required, as determined by applying Newton's second law and the work-energy principle.
Explanation:
The force required to stop the car can be found using the principles of physics, specifically by applying Newton's Second Law of motion and the formula for the work-energy principle. Initially, let's convert the car's speed from km/h to m/s by multiplying by (1000 m/1 km)(1 h/3600 s).
The resulting speed is 26.6 m/s. Utilizing the work-energy principle which states the net work done on an object is equal to the change in its kinetic energy, we can derive the equation W = ΔKE. In this case, the change in kinetic energy is the initial kinetic energy (since we're bringing the car to rest), computed as ΔKE = 0.5*mass*speed². Substituting the mass 920 kg and speed 26.6 m/s, the change in kinetic energy is about 324,074 Joules.
Since work is also calculated by the equation Work = Force*distance, we can solve for force: Force = Work / distance. Considering the stated stopping distance of 126 m, the force required thus equals 324074 J / 126 m = 2572 N. This implies an approximately 2572 N of force is needed to bring the car to rest.
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