Final answer:
To determine if the truck stops before hitting the child, we calculate the stopping distance. The truck covers 5 meters during the driver's reaction time and needs another 40 meters to stop after braking. The total stopping distance of 45 meters means the truck stops 5 meters before reaching the child.
Step-by-step explanation:
The question relates to the physics of motion, specifically the motion of a truck moving at a constant velocity of 10 m/s and its ability to stop in time when the driver sees a child 50 meters ahead. The truck has an acceleration rate of -1.25 m/s2 upon braking, and the driver's reaction time is 0.5 seconds. To determine whether the truck will hit the child, we need to calculate the stopping distance of the truck, which includes the distance covered during the driver's reaction time plus the distance it takes to stop after the brakes are applied.
The distance covered during the driver's reaction time is calculated by multiplying the truck's velocity by the reaction time: Distance = Velocity (×) Time = 10 m/s (×) 0.5 s = 5 meters.
After the reaction time, the stopping distance of the truck can be calculated using the formula: Distance = (Velocity2) / (2 (×) Acceleration). Plugging the values in gives: Distance = (10 m/s)2 / (2 (×) -1.25 m/s2) = 40 meters.
Therefore, the total stopping distance is 5 meters + 40 meters = 45 meters. Since the child is 50 meters away and the total stopping distance is 45 meters, the truck should be able to stop about 5 meters before reaching the child, thus preventing an accident. Hence, the truck will not hit the child.