To solve this problem, let's discuss the factors that influence the stopping distance of a vehicle. The stopping distance is generally split into two components:
1. Reaction Distance: This is the distance the vehicle travels from the moment a driver sees a hazard until they apply the brakes. This distance depends on the reaction time of the driver and the speed at which the vehicle is traveling. The reaction distance can be calculated with the formula:
Reaction Distance = Speed × Reaction Time
With an average reaction time for a driver being about 1.5 seconds, you can calculate the reaction distance for any given speed.
2. Braking Distance: This is the distance required for the vehicle to come to a complete stop once the brakes are applied. This distance depends on the vehicle's speed, the vehicle's braking capacity, the road condition, and the coefficient of friction between the tires and the road.
There's a more complex formula to calculate the braking distance if we know the coefficient of friction and braking efficiency, but in this case, we will rely on average stopping distance charts based on empirical data.
From driving safety studies and general guidelines, it is usually accepted that at 20 miles per hour, a vehicle will have a stopping distance of around 40 feet under normal driving conditions. As speed increases, the stopping distance increases exponentially, not linearly, due to the formula for kinetic energy which involves the square of the speed.
At 30 miles per hour, a car will typically need 75 to 90 feet to stop. So, at that speed, you will not be able to stop within 60-65 feet safely.
Given that the data for 40 miles per hour or 50 miles per hour would require even greater stopping distances, the only possible answer from the choices given that would allow your vehicle to stop within 60 to 65 feet is traveling at 20 miles per hour. At this speed, both reaction distance and braking distance would likely allow you to stop in time to avoid a collision with the child.
Hence, the correct answer would be:
- 20 miles per hour
