Final answer:
The stopping distance of a 2,000 kg car when a force of -2,000 N is applied and the car is traveling at 20 m/s is 200 meters. This is calculated using the work-energy principle, which relates the car's kinetic energy to the work done by the brakes to stop the car.
Step-by-step explanation:
The stopping distance for a 2,000 kg car when a force of -2,000 N is applied and the car is traveling at 20 m/s can be found using the work-energy principle. This principle states that the work done by the brakes is equal to the kinetic energy the car had before decelerating to a stop. To solve this, we first need to calculate the initial kinetic energy (KE) of the car using the formula KE = (1/2)mv², where 'm' is the mass of the car and 'v' is its velocity.
For the car in question:
KE = (1/2)(2000 kg)(20 m/s)² = (1000 kg)(400 m²/s²) = 400,000 joules
The work done by the brakes (W) is equal to the force applied times the stopping distance (d), so W = Force x distance. Since the work done by the brakes is equal to the car's initial kinetic energy, we can set them equal and solve for the stopping distance:
400,000 J = -2,000 N x d
d = 400,000 J / -2,000 N = -200 m
The negative sign indicates the direction of the force opposite to the motion. Since distance cannot be negative, we take the absolute value and the stopping distance is 200 m. Therefore, the correct answer is D. 200m.