Final answer:
To stop a 1000 kg car traveling at 18 m/s with a braking force of 4000 N, the deceleration is 4 m/s². Using a kinematic equation, the calculated stopping distance is 40.5 m, which does not match any of the provided multiple-choice options.
Step-by-step explanation:
To find the minimum distance required for a 1000 kg car to stop when traveling at 18 m/s with brakes applying a force of 4000 N, we must first calculate the car's deceleration. Using Newton's second law (F = ma), we get the following:
- Deceleration (a) = Force (F) / Mass (m) = 4000 N / 1000 kg = 4 m/s². Note, the acceleration is negative since it's deceleration.
Now, with the initial velocity (vi) = 18 m/s, final velocity (vf) = 0 m/s (since the car stops), and acceleration (a) = -4 m/s², we use the kinematic equation:
vf² = vi² + 2a(x)
Where x is the distance. Rearranging the equation to solve for x, we get:
0 = 18² - 2(4)(x)
x = 18² / 8
x = 324 / 8
x = 40.5 m
Therefore, the minimum distance required for the car to stop is 40.5 m. However, this option is not provided in the multiple choices A. 80 m, B. 90 m, C. 100 m, D. 120 m, indicating there might be an error in the question or the options provided. The student needs to review the question or the options.