Final answer:
To calculate at what distance from the child the motorist will stop, kinematic equations are used, involving conversion from km/hr to m/s, and then finding the deceleration and the stopping distance.
Step-by-step explanation:
The question pertains to the stoppage distance of a motorist who notices a child in his path while driving at a certain speed and then applies the brakes. To solve this problem, one would need to use the concepts of kinematics, specifically equations of motion.
First, we convert the speed from km/hr to m/s by multiplying by 5/18, which gives us 25 m/s. Then using the formula v² = u² + 2as (where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance), we set v to 0 (since the car comes to rest) and solve for s.
The initial velocity (u) is 25 m/s and the time (t) taken to stop is 20 seconds. We can find the acceleration (a) using the formula a = (v - u) / t, which gives us a negative value indicating deceleration. Substituting these values into the equation for distance, we can solve for s, which represents the stopping distance. We'll subtract this distance from the original 255m gap to find the remaining distance from the child when the motorist stops.