The braking​ distance, D, in feet required to stop a car traveling x miles per hour on​ dry, level pavement can be approximated by...

Question

D = 1/2(x^2)

A) Calculate the braking distance for a car traveling 50 miles per hour and 100 miles per hour. How do your answers​ compare? Do they octuples, nonuples, triples, doubles, or quadruples. Please explain the meaning of those.

B) If the braking distance is 25 ​feet, estimate the speed of the car.

C) If you have a​ calculator, use it to solve part​ (b) numerically. Do your answers​ agree?

Answer 1

A) Using the given formula,

for x = 50 mph

D = 1,250 feet

for x = 100 mph

D = 5,000 feet

B) The stopping distance quadrupled, in other words increased by a factor of four.

octuple = factor of 8

nontuple = factor of 9

quadruple = factor of four.

For x = 25 mph we expect a stopping distance that is 4 times less than the distance at 50 mph, so

x = 25 => D = 1,250 feet / 4 = 312.5 feet.

C) for x = 25 mph, D = (1/2)*x*x = 312.5 feet as expected.