A car is traveling 20 m/s when the driver sees a child standing on the road. He takes 0.8 s to react, then steps on the brakes and slows at 7.0 m/s2. How far does the car go before it stops?

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To find the distance traveled by the car before it stops, we need to consider two things: the distance covered during the driver's reaction time and the distance covered during braking.

1. Distance covered during the reaction time:
During the reaction time of 0.8 seconds, the car continues to move at a constant velocity of 20 m/s. Therefore, the distance covered during this time can be calculated using the formula:
Distance = Velocity × Time

Distance = (20 m/s) × (0.8 s)
Distance = 16 meters

Therefore, the car covers 16 meters during the driver's reaction time.

2. Distance covered during braking:
To calculate the distance covered during braking, we need to use the equation of motion:
Final velocity^2 = Initial velocity^2 + 2 × Acceleration × Distance

Let's assume the car comes to a stop after a distance 'd'.

Using the equation of motion, we can rearrange it to solve for distance:
Distance = (Final velocity^2 - Initial velocity^2) / (2 × Acceleration)

Substituting the given values:
Distance = (0 - (20 m/s)^2) / (2 × (-7.0 m/s^2))
Distance = (-400 m^2/s^2) / (-14.0 m/s^2)
Distance ≈ 28.57 meters

Therefore, the car covers approximately 28.57 meters during braking.

Total distance covered by the car before it stops is the sum of the distance during the reaction time and the distance during braking:
Total Distance = Distance during reaction time + Distance during braking
Total Distance = 16 meters + 28.57 meters
Total Distance ≈ 44.57 meters

So, the car travels approximately 44.57 meters before it comes to a stop.