a 2250 kg car is traveling at 20 m/s to the west. the force required to stop the car at 7890 N to the east. How long will it take the car to stop? How far would the car move before stopping?

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To solve this problem, we can use the equation for calculating the time it takes for an object to stop, which is:

Time = (Final velocity - Initial velocity) / Acceleration

First, we need to find the acceleration of the car. We can use Newton's second law of motion, which states:

Force = Mass × Acceleration

Since the car is decelerating, the force required to stop the car is negative. Therefore:

-7890 N = 2250 kg × Acceleration

Solving for Acceleration:

Acceleration = (-7890 N) / (2250 kg)

Acceleration ≈ -3.5078 m/s^2

Note that the negative sign indicates that the acceleration is directed opposite to the car's initial direction of motion.

Now, we can calculate the time it takes for the car to stop:

Time = (0 m/s - 20 m/s) / (-3.5078 m/s^2)

Time ≈ 5.70 seconds (rounded to two decimal places)

To find the distance the car moves before stopping, we can use the equation:

Distance = (Initial velocity × Time) + (0.5 × Acceleration × Time^2)

Substituting the known values:

Distance = (20 m/s × 5.70 s) + (0.5 × (-3.5078 m/s^2) × (5.70 s)^2)

Distance ≈ 57.10 meters (rounded to two decimal places)

Therefore, it will take approximately 5.70 seconds for the car to stop, and it will move about 57.10 meters before coming to a complete halt.