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Answer :
Final answer:
To find the magnitude of the braking force, we can use Newton's second law of motion which states that force is equal to mass times acceleration. Convert the speed from miles per hour to meters per second. Calculate the acceleration using the equation a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time taken to come to rest. Multiply the mass of the car by the acceleration to find the magnitude of the braking force.
Explanation:
In order to find the magnitude of the braking force, we can use Newton's second law of motion which states that force is equal to mass times acceleration. First, we need to convert the speed from miles per hour to meters per second. Then, we can use the equation f = ma to find the acceleration. Finally, we can calculate the force by multiplying the mass of the car by the acceleration.
- Convert the speed from miles per hour (mph) to meters per second (m/s). Since 1 mph is equal to 0.44704 m/s, the speed of the car is 39.16304 m/s.
- Calculate the acceleration using the equation a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time taken to come to rest. Since the car comes to rest, the final velocity is 0, the initial velocity is 39.16304 m/s, and the time taken is unknown. Therefore, we cannot calculate the actual value of the acceleration, but we can find it relative to the units used in the problem.
- Multiply the mass of the car by the acceleration to find the magnitude of the braking force. The mass of the car is 1,375 kg, and the acceleration is calculated as explained in the previous step. For the purpose of the problem, let's assume the acceleration is -1 m/s² (since it is not provided). Therefore, the magnitude of the braking force is 1,375 N.
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