Assume that the stopping distance of a van varies directly with the square of the speed. A van traveling 40 miles per hour can stop in 40 feet. If the van is traveling 72 miles per hour, what is its stopping distance?
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Since the distance varies as the square of the speed, we can express this relationship as:
d = k*s^2 where k = a constant
For two sets of distances and speeds (d1,s1) and (d2,s2) we can write
d1 = k*s1^2 and
d2 = k*s2^2
Thus d1/s1^2 = d2/s2^2 -> d2 = d1*(s2/s1)^2
Putting in the values, we have
d2 = 30*(28/20)^2 = 58.8 ft
Step-by-step explanation:
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