A car is traveling 28 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 6.5 m/s2. How far does the car go before it stops?

To calculate the distance the car goes before it stops, we can break down the problem into three parts: the reaction time, the time it takes to stop, and the distance covered during the stopping time.

1. Reaction Time:
The car is traveling at a speed of 28 m/s, and it takes the driver 0.8 seconds to react. During this time, the car covers a distance equal to the product of its initial velocity and the reaction time. Therefore, the distance covered during the reaction time is given by:
Distance = Initial velocity x Reaction time

Distance = 28 m/s x 0.8 s = 22.4 meters

2. Stopping Time:
After the reaction time, the driver steps on the brakes, and the car starts to slow down. The car decelerates at a rate of 6.5 m/s^2. We need to find the stopping time, which can be calculated using the following equation of motion:
Final velocity = Initial velocity + (Acceleration x Time)

Since the car comes to a complete stop, the final velocity is 0 m/s. Therefore, we can rewrite the equation as:
0 m/s = 28 m/s + (Acceleration x Time)

Rearranging the equation, we get:
Acceleration x Time = -28 m/s

Time = (-28 m/s) / (Acceleration)

Time = (-28 m/s) / (-6.5 m/s^2) ≈ 4.31 seconds (rounded to two decimal places)

3. Distance Covered during Stopping Time:
Finally, we can calculate the distance covered during the stopping time using the equation of motion:
Distance = Initial velocity x Time + (1/2) x (Acceleration) x (Time^2)

Distance = 28 m/s x 4.31 s + (1/2) x (-6.5 m/s^2) x (4.31 s)^2

Distance ≈ 60.49 meters (rounded to two decimal places)

Therefore, the car will travel approximately 60.49 meters before it comes to a stop.