Final answer:
The constant braking force required to bring a 100 kg car moving at 80 km/hr to rest in 100 m is calculated using the work-energy principle and is found to be approximately 246.91 N. The closest answer to this, as per the available choices, is 200 N.
Step-by-step explanation:
The question asks for the constant braking force required to bring a 100 kg car to rest from a speed of 80 km/hr over a distance of 100 meters. This is a physics problem involving kinematic equations and concepts like work and energy.
To solve this, we should first convert the speed to meters per second by dividing by 3.6 (since 1 km/hr is approximately 0.27778 m/s): 80 km/hr ÷ 3.6 = 22.22 m/s. Then, we can use the work-energy principle which states that work done by the brakes is equal to the change in kinetic energy of the car.
The kinetic energy (KE) of the car can be calculated using the formula KE = ½mv², where m is mass and v is velocity. So KE = ½ * 100 kg * (22.22 m/s)² = 24,691.11 Joules.
Since work done (W) is also the force (F) times the distance (d), and the work done is equal to the change in kinetic energy, we have F * d = KE. Rearranging that to solve for F gives us F = KE / d = 24,691.11 J ÷ 100 m = 246.91 N. So, the closest answer from the options given is Answer C. 200 N, assuming we have to select from the available choices and round to the nearest hundred.