Final answer:
To calculate the stopping distance of the truck, we add the reaction distance to the braking distance. The distance covered during the driver's reaction time is 5 meters. By applying the kinematic equation for braking distance, we can determine if the truck will stop before reaching the child.
Step-by-step explanation:
To calculate how far the truck travels before stopping, we need to consider the distance the truck covers while the driver is reacting (reaction distance), as well as the distance it covers once the brakes are applied (braking distance). The truck is moving at a constant velocity of 10 m/s when the driver sees a child 50 meters ahead and reacts after 0.5 seconds, so the reaction distance is velocity multiplied by reaction time (10 m/s × 0.5 s).
The braking distance can be calculated using the formula d = v² / (2a), where v is the initial velocity and a is the acceleration. Here, the truck's initial velocity (v) is 10 m/s and the acceleration (a) is -1.25 m/s², since acceleration is negative when the truck is slowing down. Inserting these values gives us the braking distance.
The total distance the truck covers is the sum of the reaction distance and the braking distance, which will be dAB + dBC meters. We're also given that the child is 50 meters ahead and that the truck will not hit the child. The information implies that the total stopping distance must be less than 50 meters.