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 find the distance the car goes before it stops, we need to calculate the distance covered during the reaction time and the distance covered during the braking process.
1. First, calculate the distance covered during the reaction time:
- The car is traveling at a constant speed of 28 m/s during the reaction time of 0.8 s.
- The formula to calculate distance is: distance = speed × time.
- So, distance covered during reaction time = 28 m/s × 0.8 s = 22.4 meters.
2. Next, calculate the distance covered during the braking process:
- The car is decelerating at a rate of 6.5 m/s^2.
- The formula to calculate distance when decelerating is: distance = (speed^2 - initial speed^2) / (2 × acceleration).
- The initial speed is 28 m/s and the final speed is 0 m/s (since the car stops).
- So, distance covered during braking = (0 m/s)^2 - (28 m/s)^2 / (2 × -6.5 m/s^2).
- Solving this equation:
distance = (-784 m^2/s^2) / (-13 m/s^2)
distance = 60.31 meters.
3. Finally, find the total distance covered:
- The total distance covered before the car stops is the sum of the distances covered during reaction time and braking.
- Total distance = distance during reaction time + distance during braking.
- Total distance = 22.4 meters + 60.31 meters.
- Total distance = 82.71 meters.
Therefore, the car will travel a total distance of 82.71 meters before it stops.