Final answer:
To stop a 1000 kg car traveling at 20 m/s over 48 meters, the driver applied a braking force of 4166.67 Newtons.
Step-by-step explanation:
To calculate the braking force applied by the driver to bring a 1000 kg car traveling at 20 meters per second to a complete stop over a distance of 48 meters, we can use the work-energy principle. The work done by the braking force is equal to the change in kinetic energy of the car.
We first find the initial kinetic energy (KE) using the formula KE = ½ mv², where m is the mass of the car and v is its velocity. Plugging in the values, we get KE = ½ × 1000 kg × (20 m/s)² = 200,000 Joules.
The work done by the brakes (W) is the force (F) times the stopping distance (d), which is equal to the change in kinetic energy. Therefore, W = F × d = -KE (negative because the force is in the opposite direction to the velocity). Solving for F gives us F = -KE / d = -200,000 J / 48 m = -4166.67 N. The negative sign indicates that the force is opposite to the direction of travel—the direction of emergency braking.
Therefore, the braking force that was applied to stop the car was 4166.67 Newtons.