SOLUTION: The data given below provides the distance required for a particular type of car to stop when traveling at a variety of speeds. A reasonable model for braking distance is d=as^k, w

Question 1176850: The data given below provides the distance required for a particular type of car to stop when traveling at a variety of speeds. A reasonable model for braking distance is d=as^k, where d is distance, s is speed, and a and k are constants. Use the data in the table to find values for a and k, and also type out the equation that models the breaking distance.
Speed (MPH) 10 20 30 40
Distance (Feed)5.5 22 49.5 88
a=
k=
Model:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
5.5=a10^k
a=5.5/10^k
22=a20^k
a=22/20^k
set those two equal
(5.5/10^k)=(22/20^k)
1/10^k=4/20^k
(2^k)=4
k=2
a=0.055
-
check in third where 49.5=0.055^30^2, which is true, as is the fourth.
a=0.055
k=2
Model is distance = 0.055*speed^2
d=0.55*s^2

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