Final answer:
Using the principles of physics, the shortest stopping distance for the car with a mass of 1500 kg moving at 18 m/s with a maximum friction force of 7000 N on a gravel road is calculated to be approximately 34.92 meters.
Step-by-step explanation:
Calculating the Shortest Stopping Distance
The student's question requires the application of physics principles, specifically Newton's laws of motion and kinematics, to calculate the shortest stopping distance of a car. Given the mass of the car (1500 kg) and the maximum friction force on a gravel road (7000 N), along with the initial velocity (18 m/s), we can find the stopping distance using the work-energy principle or kinematic equations.
First, we calculate the deceleration (a) using the formula a = F/m, where F is the maximum friction force and m is the mass. Substituting the given values gives us a = 7000 N / 1500 kg = 4.67 m/s². Now, using the kinematic equation v² = u² + 2as, where v is the final velocity (0 m/s for stopping), u is the initial velocity, and s is the stopping distance, we can solve for s:
s = (v² - u²) / (2a) → s = (0 - (18 m/s)²) / (2 × (-4.67 m/s²)) → s = 34.92 m
The shortest distance in which the car can stop safely is approximately 34.92 meters.