To find the magnitude of the force that stops the car, we can use Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration.
First, we need to convert the car's weight from Newtons to kilograms, since the formula requires mass in kilograms. We can do this by dividing the weight by the acceleration due to gravity (9.8 m/s^2):
Weight = 14600.0 N
Mass = Weight / Acceleration due to gravity
Mass = 14600.0 N / 9.8 m/s^2
Mass = 1489.8 kg (rounded to 3 decimal places)
Next, we need to convert the initial speed from kilometers per hour to meters per second, since the formula requires speed in meters per second. We can do this by multiplying the speed (in km/hr) by 1000/3600:
Initial speed = 58.0 km/hr
Initial speed = 58.0 km/hr * (1000 m / 3600 s)
Initial speed = 16.111 m/s (rounded to 3 decimal places)
To find the acceleration of the car, we can use the formula:
Acceleration = (Final speed - Initial speed) / Time
The car comes to a stop, so the final speed is 0 m/s.
Final speed = 0 m/s
Time = 4.7 s
Acceleration = (0 m/s - 16.111 m/s) / 4.7 s
Acceleration = -16.111 m/s / 4.7 s
Acceleration = -3.431 m/s^2 (rounded to 3 decimal places)
Now, we can use Newton's second law of motion to find the force:
Force = Mass * Acceleration
Force = 1489.8 kg * -3.431 m/s^2
Force = -5101.488 N (rounded to 3 decimal places)
The magnitude of the force that stops the car is 5101.488 N.