The speed limit in a school zone is 38 km/h. A driver traveling at this speed sees a child run onto the road 16 m ahead of his car. He applies the brakes, and the car decelerates at a uniform rate of 8.5 m/s2. If the driver's reaction time is 0.55 s, What is the stopping distance of the vehicle?

X = Stopping distance

= (reaction time)*Vo + Vo^2/(2a)
The second term of that sum is the distance travelled while decelerating.

Make sure Vo is in m/s.
38 km/h = 10.56 m/s

X = 5.51 m + 6.56 = 12.07 m

To find the stopping distance of the vehicle, we need to consider two parts: the distance the vehicle covers during the driver's reaction time and the distance it takes for the vehicle to come to a complete stop after the brakes are applied.

1. Distance covered during the driver's reaction time:
The driver's reaction time is 0.55 s. During this time, the vehicle will still be moving at the initial speed. We can calculate the distance covered during this time using the formula:
Distance = (Initial velocity) x (Time)
The initial velocity is given as 38 km/h. To convert it to m/s, we divide by 3.6:
Initial velocity = 38 km/h ÷ 3.6 = 10.56 m/s
Distance = 10.56 m/s x 0.55 s = 5.81 m

2. Distance covered to come to a complete stop:
To find the stopping distance, we need to calculate the time it takes for the vehicle to stop and then use this time to calculate the distance covered.
The car decelerates at a uniform rate of 8.5 m/s². We can find the time it takes to stop using the formula:
Time = (Final velocity - Initial velocity) ÷ (Deceleration)
The final velocity is 0 m/s (because the car comes to a complete stop). The initial velocity is 10.56 m/s. The deceleration is given as 8.5 m/s².
Time = (0 m/s - 10.56 m/s) ÷ (-8.5 m/s²) = 1.24 seconds
Now, we can calculate the distance covered during this time using the formula:
Distance = (Initial velocity) x (Time) + (0.5) x (Deceleration) x (Time)²
Distance = 10.56 m/s x 1.24 s + 0.5 x (-8.5 m/s²) x (1.24 s)² = 8.32 m

Finally, we can calculate the total stopping distance by adding the distance covered during the driver's reaction time with the distance covered to come to a complete stop:
Total Stopping Distance = 5.81 m + 8.32 m = 14.13 m

Therefore, the stopping distance of the vehicle is 14.13 meters.