Question 1078623: The braking distance of a vehicle is directly proportional to the square of its speed. when the speed of the vehicle is b m/s, its braking distance is d m. if the speed of the vehicle is increased by 200%, find the percentage increase in its braking distance.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! braking distance is directly proportional to the square of its speed.
let y = braking distance.
let x = speed.
formula is y = kx^2
when the speed is b meters per second, the braking distance is d meters.
therefore the same formula becomes d = kb^2
k is the constant of variation and never changes once initially ste up.
if the speed of the vehicle is increased by 200%, find the percentage increase in the braking distance.
an increase in the speed of 200% means that the new speed is 3 times the original speed.
therefore, the formula for d becomes d = k*(3b)^2
simplify this to get d = k*9b^2
therefore, the ratio of the new distance divided by the old distance is k * 9b^2 / k * b^2
simplify to get the ratio of the new distance to the old distance is 9/1
this means that the increase in the distance is 800% because 9/1 - 1/1 = 8/1 = 800%.
to see if this works, let's try an arbitrary example.
assume the car is traveling at 30 meters per second.
assume it takes the car 1200 meters to stop when it is traveling at 30 miles per hour.
d = k * b^2 becomes 1200 = k * 900
solve for k to get k = 1200/900 = 12/9 = 4/3
k is the constant of variation.
now assume the speed is increased by 200%.
that means it's increased by 60 meters per second.
that means the car is traveling 90 meters per second.
the formula becomes d = 4/3 * 90^2
this gets you d = 10800 meters.
it originally took 1200 meters to stop at 30 meters per second and now it takes 10800 meters at 90 meters per second.
10800 - 1200 equals an increase of 9600 meters.
9600 / 1200 = an increase of 8 times which is an increase of 800%.
looks like the formula works.
an increase of 200% in the speed results in an increase of 800% in the stopping distance.
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