Suppose a car is traveling at 17.0 m/s, and the driver sees a traffic light turn red. After 0.570 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 9.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light?

To find the stopping distance of the car, we need to calculate two distances: the distance traveled during the driver's reaction time and the distance traveled while decelerating.

First, let's calculate the distance traveled during the driver's reaction time. We know that the car is traveling at 17.0 m/s for 0.570 s. The formula to calculate distance is:

distance = speed × time

So, the distance traveled during the reaction time is:

distance1 = 17.0 m/s × 0.570 s

Next, let's calculate the distance traveled while decelerating. The formula to calculate the distance is:

distance = (initial speed × time) + (0.5 × acceleration × time^2)

In this case, the initial speed is 17.0 m/s, the time is the total time minus the reaction time (since the deceleration starts after the reaction time), and the acceleration is -9.00 m/s² (negative because it's a deceleration). Let's call the time after the reaction time as t:

distance2 = (17.0 m/s × t) + (0.5 × (-9.00 m/s²) × t²)

Now, let's substitute t with the total time minus the reaction time:

distance2 = (17.0 m/s × (0.570 s - t)) + (0.5 × (-9.00 m/s²) × (0.570 s - t)²)

Now, the stopping distance is the sum of distance1 and distance2:

stopping distance = distance1 + distance2

You can calculate the stopping distance by plugging in the values and solving the equation.

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