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An automobile traveling at a speed of 29.2 m/s applies its brakes and comes to a stop in 4.96 s. If the automobile has a mass of 1.39 × 103 kg, what is the average horizontal force exerted on it during braking? Assume the road is level. Enter a positive answer if the force is with the car's direction of motion, and a negative answer if it is opposite the car's direction of motion.

Question

An automobile traveling at a speed of 29.2 m/s applies its brakes and comes to a stop in 4.96 s. If the automobile has a mass of 1.39 × 103 kg, what is the average horizontal force exerted on it during braking? Assume the road is level. Enter a positive answer if the force is with the car's direction of motion, and a negative answer if it is opposite the car's direction of motion.

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Solution

To solve this problem, we need to use the formula for force, which is mass times acceleration (F = ma). However, we don't have the acceleration, so we need to calculate it first.

Acceleration is the change in velocity over time (a = Δv/Δt). In this case, the change in velocity is the final velocity minus the initial velocity. Since the car comes to a stop, the final velocity is 0 m/s. The initial velocity is given as 29.2 m/s.

So, the acceleration is a = (0 m/s - 29.2 m/s) / 4.96 s = -5.89 m/s². The negative sign indicates that this is a deceleration, or a slowing down, which makes sense because the car is stopping.

Now we can calculate the force. The mass of the car is given as 1.39 × 10³ kg. So, the force is F = (1.39 × 10³ kg) * (-5.89 m/s²) = -8181 N.

The negative sign indicates that the force is in the opposite direction of the car's initial motion, which makes sense because the force is what's stopping the car. So, the average horizontal force exerted on the car during braking is -8181 N.

This problem has been solved

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