An automobile traveling at a speed of 28.1 m/s applies its brakes and comes to a stop in 4.9 s. If the automobile has a mass of 9.0 102 kg, what is the average horizontal force exerted on it during braking? Assume the road is level.

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, but we can calculate it using the formula for acceleration, which is change in velocity divided by time (a = Δv/t).

Step 1: Calculate the acceleration The initial velocity (v_i) is 28.1 m/s, the final velocity (v_f) is 0 m/s (since the car comes to a stop), and the time (t) is 4.9 s. So, the acceleration (a) is:

a = (v_f - v_i) / t a = (0 m/s - 28.1 m/s) / 4.9 s a = -28.1 m/s / 4.9 s a = -5.73 m/s²

The negative sign indicates that this is a deceleration, or slowing down, which makes sense because the car is stopping.

Step 2: Calculate the force Now that we have the acceleration, we can calculate the force. The mass (m) of the car is 9.0 x 10² kg, so the force (F) is:

F = m * a F = 9.0 x 10² kg * -5.73 m/s² F = -5157 N

The negative sign indicates that the force is acting 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 5157 N.