Final answer:
To find the constant of proportionality for Mallory's car stopping distance, we use the formula d = kv². Solving for k with provided values, we discover that k is about 0.0765 m³/s².
Step-by-step explanation:
The question at hand is focused on finding the constant of proportionality in the context of a car's stopping distance. This involves understanding that the stopping distance (d) is directly proportional to the square of the speed (v) of the vehicle, commonly expressed in the form d = kv2, where k is the constant of proportionality. Mallory's stopping distance at 70 miles per hour (which converts to approximately 31.2928 meters per second) is 245 feet (which converts to 74.676 meters). We need to solve for k using the formula:
d = kv2
74.676 = k(31.2928)2
k = 74.676 / (31.2928)2
After calculating, we find that the value of the constant of proportionality k is roughly 0.0765 m3/s2 or 0.0765 meters per second squared per foot.