SOLUTION: The stopping distance (D) of a vehicle varies directly as the square of its velocity (V). If a vehicle traveling 40 mph requires 100 feet to come to a stop, find the stopping dist

Question 673595: The stopping distance (D) of a vehicle varies directly as the square of its velocity (V). If a vehicle traveling 40 mph requires 100 feet to come to a stop, find the stopping distance of a vehicle traveling 60 mph.
I started with y=kx for "varies directly" and did not know where to go from there. Also, I am not sure that I am using the correct method in considering this problem. The "square of its velocity" is throwing me off.
Found 2 solutions by sachi, MathTherapy:
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!
stopping distance (D) of a vehicle varies directly as the square of its velocity (V)
so D/V2=const
or 100/(40)2=D/(60)2
or D=100*(60/40)2=150 feet
ans
Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!

The stopping distance (D) of a vehicle varies directly as the square of its velocity (V). If a vehicle traveling 40 mph requires 100 feet to come to a stop, find the stopping distance of a vehicle traveling 60 mph.

Since the stopping distance varies directly as the square of its velocity (V), then:

, with k being the constant of variation

100 = 1,600k

k = , or

D, or stopping distance = ft

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